Quantum Insights o Primordial Black Holes as Dak Mate
Francesca Vidotto UPV/EHU - Bilbao
2ND WORLD SUMMIT ON EXPLORING THE DARK SIDE OF THE UNIVERSE Guadalupe Island - June 29th, 2018 THE DARK SIDE OF GRAVITY Caution: not a complete list!
DARK ENERGY Cosmological Constant (or more complicated GR modification)
Gravitational Backreaction see Buchert’s talk Quantum Gravity: Spacetime Discreteness Perez, Sudarsky, Bjorken 1804.07162 …
DARK MATTER Mond, Mimetic Gravity and other classical modification of GR
Bimetric Gravity see Henry-Couannier’s talk N-body Equivalence Principle Alexander, Smolin 1804.09573 Quantum Gravity: Minimal Acceleration Smolin 1704.00780
Emergent Gravity Verlinde 1611.02269 …
Primordial Black Holes see also Garcia-Bellido’s talk
Quantum Gravity Phenomenology Francesca Vidotto PRIMORDIAL BLACK HOLES
PBHs are the least exotic beast in the dark universe zoo of theories
PBHs are a viable DARK MATTER candidate * careful with old constraints in the literature!
PBHs are interesting even if they are not all DARK MATTER * PBHs can be used to test QUANTUM GRAVITY
Quantum Gravity Phenomenology Francesca Vidotto IN THIS TALK: QUANTUM GRAVITY
1. QG makes PBH remnants stable * Quantum Gravity: minimal aerea
2. QG cures GR singularities * NO central BH singularity, NO cosmological singularity: instead a bounce
3. QG allows for Black-to-White tunnelling * Decay happens faster than the Hawking evaporation: new phenomenology
3 different scenarios discussed in this talk
Quantum Gravity Phenomenology Francesca Vidotto 5 governed by the Hamiltonian where we have taken the Immirzi parameter to be unit
2 for simplicity. The minimal non-vanishing eigenvalue is p 2 @ ~ @ ~ m +3 3 i⇡mo @v i m2 @m b m H = ao =4p3⇡ G (24) 0 m2/ 2 @ 1 ~ c ~ e ~ m 3p3 i⇡m
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12)
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is due to the fact that process (1) does not a↵ect the the
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WHITE HOLES AS REMNANTS 1 (2.
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QUANTUM EFFECTS MAKE REMNANTS STABLEthe
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to
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us
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˜ that explicitly
solution
other
solution
expansion
other
that explicitly that
that solution
other expansion
explicitly
expansion
—
an
explicitly
— an
— —
metric
an
for
for
metric
an
metric
Oat
for for
metric
for
for
for Oat
Oat for
and project down to a smaller state space with ba- Oat
but
in
symmetric
field but
in
the
arbitrary any
in
field symmetric
but
in
the
symmetric any
arbitrary dilaton,
of
dH+a(r)
as
but symmetric
field dependence
by breaks time reversal invariance is the notion of stability the
arbitrary
any dilaton,
of
as
dH+a(r)
the
dependence
field arbitrary
undetermined. by
dilaton,
dynamics
of
dH+a(r)
any
as by
dilaton, of
dH+a(r)
of dependence
undetermined.
dynamics
by
we of
as
undetermined. dynamics
dependence
up
dynamics
we
undetermined.
everywhere
of
around
up
we
a everywhere
around
up
of patching
Our
we
a
up
a
everywhere
around
patching
the Our
form
a
a
for
everywhere
around
patching
a
Our
the
H H form
perturbatively,
a a
for
smooth a
patching
assuming motion
a
Our
the
sensible
form a
perturbatively, a
coefficient
smooth
for
we
motion assuming
finite
the
form sensible
this
a
coefficient
perturbatively,
equations
smooth
a
we
for
assuming
have finite
motion
finite collapsing
this
sensible
We
equations
a with
smooth
coefficient
perturbatively,
assuming
have
shown a
collapsing
motion we
finite
finite
with
this
We
sensible
with
finite
coefficient
shown
equations to
sis states H, µ . This is a two dimensional Hilbert space functions
finite
have
we
finite with collapsing
this
finite
with
We
to
functions
finite
equations
collapsing
shown
all
have
so
that we are using. This is a stability under small fluc- with
ordinary collapsing
with
We
finite
to
functions matching of collapsing
all
shown
so
with
ordinary
feel
to
matching of
functions
finite
the
collapsing
all
so
is
in demonstration
of
ordinary
feel
with
the
matching of
collapsing
assumption
is
all
in demonstration
the
can so
of
ordinary
with
time
feel
of
| i matching
finite
the
described,
obtained
assumption keep
the
can
is
in
of demonstration
the
a
time
the
with
region.
finite
inconsistent.
described,
feel
obtained
keep
(dr
the
assumption
of
powers
is
the
the
gives can
of
in
solutions the
a
in
demonstration
the
region.
with
inconsistent.
volume
time
ansatz
(dr
finite
keep
obtained
described,
of
powers
solutions assumption
with basis vectors B,µ and W, µ . Seen from the exte- gives
in
in
solutions the existence occurs
the
can the
confident
a
natural
volume the
region. ansatz
inconsistent.
shell,
time
keep (dr
finite solutions
tuations of the past boundary conditions. If instead we obtained in
described, a
occurs existence
of
powers
confident gives
solutions
the in
the
natural the
smooth
then
the a
the
a
region.
shell,
cornucopion.
volume inconsistent.
ansatz
that
topology
(dr
a
functions,
vacuum
solutions
after
of
gives
the
in powers
smooth existence
solutions
occurs then
the the
in
confident
a cornucopion. Fig.
natural
cosmological +r
metric,
that
topology
shell, values
functions, volume
ansatz
vacuum
nonsingular
after
and
a
solutions
| i | i Fig.
Thus
existence in the
occurs
the cosmological
+r
smooth
then
confident
natural
differential
metric,
the
a
values
cornucopion.
nonsingular
shell,
shell,
and
topology
that
conditions functions,
vacuum
a
collapsing
rise
after
Thus
field
differential
the the
the
Fig.
then smooth
cosmological +r
a
shell,
metric,
to
that values
cornucopion.
does
conditions
nonsingular
topology
rior, the state of ⌃ will converge to . collapsing
rise
and
that is
of
vacuum
field functions,
µ We
use
dQ
after
Thus
behaves
only
differential
the
asked about stability under small fluctuations of the fu- cosmological +r
Fig. to
2. that
its
does
cornu- metric,
shell,
is
values of
begins
We
nonsingular
conditions
dilaton
and use
dQ
rise collapsing
ansatz. that
behaves
only
field
static
Thus
verify
2.
its
cornu-
of
the
differential
n
(2. begins
three- to
that shell, solu-
dilaton
does
to
there
ansatz. that
of
conditions
equa-
of
of exist.
is We
Bianchi, Cristodoulou, D’Ambrosio, rise
static
collapsing that
leav-
H dQ use field
verify
for-
behaves
only of
will
of
We
with
n
have
field
this
(2.
not
three-
solu-
) 2.
its
of
cornu-
are
to
there
of
to
equa- of
exist.
that
does
begins
that
dilaton
We
leav-
in
13)
We
ansatz. for-
that of
is
will dQ
of We
FIG. 2. the
use
with
static
The interior geometry of an old black hole: a very to
have
field this
behaves
in-
not
4 verify
The Hamiltonian acting on this subspace is ~.
only
)
of
of
are
a
an
a
n
(2. 47
three-
2.
its
cornu-
solu- We
in 13)
ture boundary conditions, we would obviously obtain the to
there
a
equa-
of
exist. begins dilaton
of
the
ansatz. that
Haggard, Rovelli 1802.04264to leav-
REMNANT LIFETIME ~ Mo that
in-
~.
for-
will
a
of static
We
with
an a have
verify
field
of
this
47
not
)
of
n
are
three-
a (2.
solu-
to
We
there
equa-
13) in
exist.
long thin tube, whose length increases and whose radius de- of
of
leav-
the
that
to
in-
for-
~.
will with
of
have
We
field
a
an
this
)
a
not 47
of
are
a
We 13)
in FIG. 3. The transition across the
the to
A region. in-
opposite result: macroscopic white holes would be stable ~.
an
a
creases with time. Notice it is finite, unlikely the Einstein- 47 a
Time for information to leak out from such a large volume trough the small WH surface. a while macroscopic black holes would not. Rosen bridge. µ b~ H = µ (26) a~ invariant K R Rµ⌫⇢ is easily computed to be The question we are interested in is what happens µ µ ! ⌘ µ⌫⇢ (generically) to a large macroscopic black hole if it is the two regions A and B where classical general relativity 9 l2 24 l⌧ 2 + 48 ⌧ 4 K(⌧) 2 becomes unreliable. Rovelli, Vidotto 1805.03872 2 m (5) not fed by incoming mass. ThenPROCESSES two processes are in p3 ⇡ (l + ⌧ )8 Region A is characterised4 by large curvature and covers 3 where a = ce . Quantum mechanics indicates that in place: its Hawking evaporation for1. aBH time volumem increase/~ (pro- & WH volumethe singularity. decrease According to classical general relativity in the large mass limit, which has the finite maximum ⇠ a situationthe singularity where never reaches the system the horizon. can (N.B.: radiate Two energy away and cess 3) and the internal growth of2. Whitev (process to black 1). instability This 9 m2 lines meeting at the boundary of a conformal diagram K(0) there are possible transitions between these two states, 6 . (6) continues until process (4) becomes3. Hawking relevant, evaporation which hap- does not ⇡ l the actualmean state that they will meet converge in theFrom physical the to spacetime.) aoutside, quantum at a state finite whichtime, 4. Black to white tunnelling Region B pens when the mass is reduced to order of Planck mass. , instead, surrounds no distinction the end of the evapora- between blackFor and all the white values ofholes⌧ where l ⌧ 2 < 2m the line is ation, quantum which involves superposition the horizon, and a of the two given by the lowest ⌧ At this point the black hole has a probability of order ↵ects what hap- element is well approximated by taking l = 0 which gives eigenstatepens outside of the hole.H.Thisis Taking evaporation into account, the area of the horizon shrinks progressively until reach- 4⌧ 4 2m ⌧ 2 one to tunnel into a white hole under process (4). But a ds2 = d⌧ 2 + 2 4 2 ing region B. 2 2 dx + ⌧ d⌦ . (7) STABILITY a oscillation 2 mbetween⌧ ⌧ white hole in unstable under process (2), giving it a finite The quantum gravitational e ↵bectsB,µ in regions W,A and µ B The minimal area yields a minimalare mass! distinct, and confusing them is a source of misun- Forblack⌧ < and0, this iswhite the Schwarzschild metric inside the probability of returning back to a black hole. Both pro- R = | i a| i (27) derstanding. Notice| thati a generic spacetime1+ region in black hole, as can be readily seen going to Schwarzschild cesses (4) and (2) are fast at this point. Notice that this p b coordinateshole states A is spacelike separated and in general very distant from happens at large v, therefore in a configuration that clas- region B. By locality, there is no reason to expect these 2 p ts = x, and rs = ⌧ . (8) sically is very distant from flat space,Quantum even Gravity if Phenomenology the overall (R twofor regions ‘Remnant’) to influence one and another. has eigenvalue µ ~pab/µFrancesca.If Vidotto the amplitudeThe quantum gravitationalb of going physical from process black happening to white For ⌧ is> 0, larger this is the Schwarzschild metric inside a white mass involved is small. at these two regions must be considered separately. hole. Thus the metric ( 4) represents a continuous transi- As energy is constantly radiated away and no energy than the amplitude a of going from white totion of black the geometry (as of a black hole into the geometry of it seems plausible), the state is dominated bya white the hole, white across a region of Planckian, but bounded is fed into the system, the system evolves towards low curvature. hole component.III. THE A REGION: A related TRANSITIONING picture was been considered m.Butm cannot vanish, because of the presence of the ACROSS THE SINGULARITY Geometrically, ⌧ = constant (space-like) surfaces foli- interior: in the classical theory, a geometry with larger v in [43–45]: a classical oscillation between blackate the and interior white of a black hole. Each of these surfaces has the topology 2 R, namely is a long cylinder. As and small m is not contiguous to a Minkowski geometry, holeTo states. study the A region, let us focus on an arbitrary time passes, the radialS size⇥ of the cylinder shrinks while finite portion of the collapsing interior tube. As we ap- the axis of the cylinder gets stretched. Around even if the mass is small. Therefore in the large v region Inproach a the fully singularity, stationary the Schwarzschild situation, radius the mass m is equal ⌧ =0 rs,which the cylinder reaches a minimal size, and then smoothly we have m>0. Alternatively, this can be seen as a tois the a temporal Bondi coordinate mass, inside which the hole, generates decreases and time translationsbounces back and at starts increasing its radial size and largethe curvature distance increases. from When the the hole curvature in approaches the frame determinedshrinking its length. by The cylinder never reaches zero size hypothesis ruling out macroscopic topology change. Planckian values, the classical approximation becomes but bounces at a small finite radius l. The Ricci tensor theunreliable. hole. Quantum (Quantum gravity e gravity is locally Lorentz invariant But m cannot be arbitrarily small either, because of ↵ects are expected to vanishes up to terms O(l/m). [46bound, 47] the and curvature has [ no7–10 preferred, 12–18, 21–23 time, 26, 28, [4859,]60 but]. aThe black resulting hole geometry is depicted in Figure quantum gravity. The quantity m is defined locally by Let us see what a bound on the curvature can yield. Fol- 3.The region around ⌧ = 0 is the smoothing of the central black the area of the horizon A = 16⇡G2 m2 and A is quan- inlowing a large [ 61], nearly-flat consider the line element region determines a preferred frame hole singularity at rs = 0. and a preferred time variable.) Keeping possibleThis geometry tran- can be given a simple physical interpre- tized. According to Loop Quantum Gravity [40]the 2 2 2 2 4(⌧ + l) 2 2m ⌧ tation. General relativity is not reliable at high curva- sitionsds = into accountd⌧ + there dx is2 +( a⌧ subtle2 +l)2d⌦2 di, (4)↵erence between eigenvalues of the area of any surface are [41] 2m ⌧ 2 ⌧ 2 + l ture, because of quantum gravity. Therefore the “pre- the mass m, determined locally by the horizondiction” area, of the and singularity by the classical theory has no A =8⇡ G j(j + 1) (23) thewhere energyl m. ofThis the line element system, defines which a genuine is Rieman- determinedground. by Highthe curvature full induces quantum particle cre- ~ nian spacetime,⌧ with no divergences and no singularities. ation, including gravitons, and these can have an e ↵ec- Curvature is bounded. For instance, the Kretschmann p tive energy momentum tensor that back-reacts on the Scenario 1 REHEATING Remnants
Quantum Black Holes Francesca Vidotto 2 mal extension of the Schwarzschild solution is equally the outside of a black hole and the outside of a white hole (see Fig. 1, Top). Analogous considerations hold for the 2 Kerr solution. In other words, the continuation inside the radius r =2m + ✏ of an external stationary black
mal extension of the Schwarzschild solution is equally the hole metric contains both a trapped region (a black hole) WH II outside of a black hole and the outsidead an anti-trapped of a white hole region (a white hole). BH (see Fig. 1, Top). Analogous considerationsWhat distinguishes hold for the then a black hole from a white Kerr solution. In other words, thehole? continuation The objects inside in the sky we call ‘black holes’ are de-
the radius r =2m + ✏ of an externalscribedstationary by a stationaryblack metric only approximately, and hole metric contains both a trappedfor region a limited (a black time. hole) In their past (at least) theirWH met- II ad an anti-trapped region (a whiteric hole). was definitely non-stationary, as they were producedBH What distinguishes then a blackby gravitational hole from a collapse. white In this case, the continuation of the metric inside the radius r =2m + ✏ contains a hole? The objects in the sky we call ‘black holes’ are de- FIG. 2: The full life of a black-white hole. scribed by a stationary metric onlytrapped approximately, region, but and not an anti-trapped region (see Fig. for a limited time. In their past1, (at Center). least) Viceversa, their met- a white hole is an object that is ric was definitely non-stationary,undistinguishable as they were produced from a black hole from the exterior and is longer [16]: by gravitational collapse. In thisfor case, a finite the continuation time, but in the future ceases to be stationary 4 of the metric inside the radius rand=2 therem + is✏ contains no trapped a region in its future (see Fig. 1, ⌧BH m . (2) FIG. 2: The full life of a black-white hole. ⇠ o trapped region, but not an anti-trappedBottom). region (see Fig. 1, Center). Viceversa, a white hole is an object that is The tunnelling process itself from black to white takes a undistinguishable from a black hole from the exterior and time of the order of the current mass at transition time is longer [16]: [15]. The area of the horizon of the black hole decreases for a finite time, but in the future ceasesIII. to be QUANTUM stationary PROCESSES AND TIME with time because of Hawking evaporation, decreasing and there is no trapped region in its future (see Fig. 1,SCALES 4 ⌧BH mfromo. m to the Planck(2) mass m . At this point the Bottom). ⇠ o Pl transition happens and a white hole of mass of the order The classical prediction thatThe the tunnelling black is forever process stable itself from black to white takes a of the Planck mass is formed. is not reliable. In the uppermosttime of the band order of the of the central current mass at transition time III. QUANTUM PROCESSESdiagram AND of Fig. TIME 1 quantum theory[15]. The dominates. area of theThe horizon death of the black hole decreases SCALES of a black hole is therefore awith quantum time phenomenon. because of Hawking The evaporation, decreasingIV. TIMESCALES same is true for a white hole,from reversingmo to thetime Planck direction. mass mPl. At this point the That is, the birth of a whitetransition hole is in happens a region and where a white hole of mass of the order The classical prediction that thequantum black is gravitationalforever stable phenomena are strong. Consider the hypothesis that white-hole remnants are of the Planck mass is formed. a constituent of dark matter. To give an idea of the is not reliable. In the uppermostThis band consideration of the central eliminates a traditional objection density of these objects, a local dark matter density of diagram of Fig. 1 quantum theoryto dominates. the physical The existence death of white holes: How would they of a black hole is therefore a quantum phenomenon. The the order of 0.01M /pc3 corresponds to approximately originate? They originate from a region whereIV. quantum TIMESCALES one Planck-scale remnant, with the weight of half a inch same is true for a white hole, reversingphenomena time dominate direction. the behaviour of the gravitational of human hair, per each 10.000Km3. For these objects to That is, the birth of a white holefield. is in a region where quantum gravitational phenomena are strong. Consider the hypothesis thatbe white-hole still present remnants now we are need that their lifetime be larger Such regions are generateda constituent in particular of by dark the matter. end To give an idea of the This consideration eliminates a traditional objection or equal than the Hubble time TH , that is of the life of a black hole,density as mentioned of these above. objects, Hence a local dark matter density of to the physical existence of whitea holes: white How hole would can in they principle be originated by a dying3 4 the order of 0.01M /pc corresponds to approximatelymo TH . (3) originate? They originate from ablack region hole. where This quantum scenario has been shown to be concretely one Planck-scale remnant, with the weight of half a inch phenomena dominate the behaviourcompatible of the gravitational with the exact external Einstein dynamics On the other hand, since the possibility of many larger of human hair, per each 10.000Km3. For these objects to field. in [12] and has been explored in [13–18]. The causal back holes is constrained by observation, we expect rem- be still present now we need that their lifetime be larger Such regions are generated indiagram particular of the by the spacetime end giving the full life cycle of the nants to be produced by already evaporated black holes, REMNANTSor equal than theFORMED Hubble timeAFTERTH , INFLATION that is of the life of a black hole, as mentionedblack-white above. hole is Hence given below in Fig. 2. therefore the lifetime of the black holeRovelli, must Vidotto be 1805.03872 shorter a white hole can in principle be originatedIn particular, by a the dying result of [16] indicates that the black-m4 T than. the Hubble time.(3) Therefore to-white process is asymmetric in time [13] and the timeo H black hole. This scenario has been shown to be concretely 3 compatible with the exact externalscales Einstein of the durations dynamics of theOn di the↵erent other phases hand, are since deter- the possibility of many largermo
Quantum Gravity Phenomenology Francesca Vidotto Scenario 2 BIG BOUNCE Remnants
Quantum Black Holes Francesca Vidotto 2
of the matter density ⇢M , and this in turn is related to of gravity, to which generic evolution tends, are highly TH by the Friedmann equation crumpled, not homogeneous. (For interesting criticisms and informed alternative perspectives, see [38–41].) 1 a˙ 2 ⇢ , (5) The fact that source of past low entropy, hence the T 2 ⇠ a ⇠ M source of irreversibility, was the homogeneity of space H ✓ ◆ is confirmed by a simple analysis of the thermodynam- where we neglect factors of order unit. Therefore the ical history of the universe. For instance irreversibility current density ⇢ of remnants is of the order on Earth is due to the strong source of negative en- 1 ergy formed by the sun; the sun in turn was irreversibly ⇢ ⇢M 2 . (6) formed by the collapse of a primordial cloud under grav- ⇠ ⇠ TH itational attraction. Therefore the original negative en- If we take the mass of each remnant to be Planckian tropy driving irreversibility around us can be traced to [15], namely of order unit in Planck units, ⇢ is also their the early lack of gravitational clumping. As repeatedly 2 number density in the units we are using. From the big pointed out by Penrose, the fact that the geometry of bounce to the currentof the epoch matter the density universe⇢ , has and widely this in turn ex- is relatedthe universe to of was gravity, small to and which homogenous generic evolution to the degree tends, re- are highly M quired by the current standard cosmological model, im- panded. AssumingTH atby least the Friedmann 60 e-folding, equation the bounce is crumpled, not homogeneous. (For interesting2 criticisms plies a very ‘special’and informed state alternative determining perspectives, an initial see low [38 en-–41].) not very far from the epoch where the horizon2 is Planck- 1 a˙ tropy. The fact that source of past low entropy, hence the of theian, matter which density gives⇢ aM linear, and expansion this in turn factor is related of the to order⇢ , of of gravity, to(5) which generic evolution tends, are highly BIG BOUNCE REMNANTS T 2 ⇠ a ⇠ M But if thesource remnant of scenario irreversibility, is correct, was the the homogeneity geometry at of space TH byTH theand Friedmann therefore equation a volume expansionH factor✓ ◆ of theRovelli, ordercrumpled, Vidotto 1805.03224 not homogeneous. (For interesting criticisms 3 the bounce hadis confirmed far more volumeby a simple and analysis was not of homogenous the thermodynam- of TH .Tohavethesuwhere wecient neglect density factors of remnants of order unit. todayand Therefore informed the alternative perspectives, see [38–41].) to saturate dark1 matter,a˙ 2 we need a density of the order at all. To theical opposite, history of it the was universe. very highly For instance crumpled. irreversibility If current density⇢ , ⇢ of remnants is(5) of the orderThe fact that sourceon Earth of past is low due entropy, to the strong hence source the of negative en- T 2 a M source ofso, irreversibility, what is the origin was the of past homogeneity low entropy, of space if it is not how H ⇠ ⇠ 3 ergy formed by the sun; the sun in turn was irreversibly BOUNCING BLACK HOLES IN A BOUNCING✓⇢ UNIVERSE◆ ⇢T T Quintin,1 Brandenberger(7) 1609.02556special the initial geometry was? b H H ⇢ ⇢ . is confirmed by(6) a simpleformed analysis by the collapse of the thermodynam- of a primordial cloud under grav- where we neglect factors of⇠ order unit.⇠ ThereforeM Carr, the2 Clifton, Coley 1704.02919 Planckian PBH remands from a previous eon (Penrose’s EREBONS) ⇠ ⇠ TH ical history of the universe.itational attraction. For instance Therefore irreversibility the original negative en- currentat density the bounce.⇢ of remnants Using (4) is we of the have order an amount of internalon Earth is due to the strong source of negative en- If we take the mass of each remnant to be Planckian tropy driving irreversibility around us can be traced to Planck size particles can pass troughvolume the perbounce. unit of external volume ergy formed by the sun; the sun in turn was irreversibly [15], namely1 of order unit in Planck units, ⇢ is also their IV.the PERSPECTIVAL early lack of gravitational ENTROPY clumping. As repeatedly ⇢ ⇢ . (6) formed by the collapse of a primordial cloud under grav- numberM density2 in the2 units we are using. From the big pointed out by Penrose, the fact that the geometry of ⇠Vint =⇠ ⇢TbHVWH >TH . (8) bounce to the current epoch the universeitational has widely attraction. ex- the Therefore universe the was original small and negative homogenous en- to the degree re- PAST LOW ENTROPY An imposing aspects of the Cosmos is the mighty daily If we take the mass ofpanded. each remnant Assuming to beat least Planckian 60 e-folding,tropy the driving bounce irreversibility is quired by around the current us can standard be traced cosmological to model, im- This means that only a fraction rotation of Sun,plies a Moon, very ‘special’ planets, state stars determining and all an galaxies initial low en- Matter near thermal equilibrium:[15], namely geometry of order has unitlownot entropy in very Planck far from units, the⇢ epochis also where their the horizonthe early is Planck- lack of gravitational clumping. As repeatedly tropy. A volume of the universe outsidenumber BH density as low in as the only unitsian, 1 /T which we 2 are gives 10 using. 120 a linear of From the expansion thetotal big factorpointed(9) of thearound out order by of us. Penrose, Why the does fact the that Cosmos the geometry rotate so? of Well, it is H But if the remnant scenario is correct, the geometry at bounce to the current epochTH and the therefore⇠ universe a has volume widely expansion ex- factorthe universe ofnot the order the was Cosmos small and rotating, homogenous it is us. to Thethe degree rotation re- of the sky could have been outside the remnants at the bounce! 3 quired by the currentthe standard bounce had cosmological far more volume model, and im- was not homogenous panded.of the Assuming volume of at the leastof universeTH 60.Tohavethesu e-folding, was outside the bouncecient the remnants density is of at remnantsis a todayperspectival phenomenon: we understand it better as to saturate dark matter, we need a densityplies of a verythedue order ‘special’ to the peculiarityat state all. determining To the of our opposite, own an initial moving it was low very point en- highly of view, crumpled. If not verythe far bounce. from the If we epoch assume where equiprobability the horizon is Planck- for each equal 2 tropy. rather thanso, as what a global is the feature origin of of past all low celestial entropy, objects. if it is not how ian, whichvolume gives of the a linear universe, expansion the probability factor of the for order an3 observer of to special the initial geometry was? DARK MATTER ⇢b ⇢TH TH But if the remnant(7) scenario is correct, the geometry at TH andbe therefore outside those a volume remnants expansion at the factor bounce of⇠ the is order one⇠ part in The list of conspicuous phenomena that have turned out of the matter density ⇢M , and this in turn is related to of gravity, to which generic evolution tends, are highly We want Mo4 ≥ tHubble for them3 to 120survive till today. the bounceto be had perspectival far more volume is long; and was recognising not homogenous them has been a T by the Friedmannof equationTH10.Tohavethesu. Therefore anatcient the observer density bounce. outside ofcrumpled, Using remnants (the4) we remnantsnot today have homogeneous. an amountis in of (For internal interesting criticisms H 120 at all. Topersistent the opposite, aspect it of was the very progress highly of crumpled. science. If to saturatethis sense dark ‘special’ matter,volume aswe one need per part a unit density inand of 10 external informed of. the order volume alternative perspectives, see [38–41].) 2 so, what isThe the hypothesis origin of past put lowIV. forward entropy, PERSPECTIVAL in if [26 it] is is not that how ENTROPY the increase 1 a˙ 3 The fact that source2 of past low entropy, hence the ⇢ , ⇢b ⇢T (5)TH Vint = ⇢bVWH(7)>T .special the initial(8) geometry was? Inflation dilutes PBH: T 2 ⇠ a ⇠ M ⇠ H ⇠ source of irreversibility,H was theof entropy homogeneity is a perspectival of space phenomenon in this sense. To H ✓ ◆ An imposing aspects of the Cosmos is the mighty daily III. PAST LOWis ENTROPY confirmed by a simple analysisbe sure, of the it thermodynam-is not subjective or mental, or illusory. Rather, at the bounce. Using (4This) we means have an that amount only a of fraction internal rotation of Sun, Moon, planets, stars and all galaxies where we neglect factors of order unit. Therefore the ical history of the universe. Forits instance source is irreversibility in the relation between an observer system volume per unit of external volume 2 120 around us. Why does the Cosmos rotate so? Well, it is MATTERcurrent BOUNCE: density ⇢ ofPBH remnants as pressureless is of the ordercomponent on Earth1/T is10 due to the strongandIV. source an(9) PERSPECTIVAL observed of negative system, en- like ENTROPY for the rotation of the sky. The mystery of the second principle ofH thermodynam-⇠ not the Cosmos rotating, it is us. The rotation of the sky 2 ergy formed by the sun; the sun in turn was irreversibly ics is not1 whyVint entropy= ⇢bVWH growth>TH towards. the future.(8) That’s This is possibleis a perspectival becausephenomenon: the entropy we of understand a system de- it better as ⇢ ⇢ . of the volume(6) of the universe was outside the remnants at Mpretty2 obvious. The mystery isformed why entropy by the collapse diminishes ofAn a primordial imposingpends on aspects cloud thedue under system’s of to the the grav- Cosmos peculiarity microstate is the ofbut mighty our also own dailyon moving the coarse point of view, ⇠ ⇠ TH the bounce. If we assume equiprobability for each equal This meansgoing towards that only the a fraction past [30–35].itational All current attraction. irreversible Thereforerotationgraining the of Sun, original under Moon,rather negative which planets, than en- the as stars system a global and interacts. feature all galaxies of The all celestialrelevant objects. volume of the universe,tropy driving the probability irreversibility for an around observer us to can be traced to If we take the mass of eachphenomena, remnant to including bebe2 Planckian outside our120 own those future-oriented remnants at the thinking, bouncearound is onecoarse us. part Why in graining doesThe the islist Cosmos determined of conspicuous rotate by so? phenomena the Well, concrete it that is existing have turned out 1/TH 10 the early lack of(9) gravitational clumping. As repeatedly Quantum [Gravity15], namely Phenomenology of order unit inthe Planck existence units, of⇢ is memories10 also120⇠. their Therefore and the an observerdirection outside of causal- thenotFrancesca remnants the Cosmosinteractions Vidotto is in rotating,to with be it the perspectival is us. system. The rotation is The long; entropy recognising of the sky we assign them has to been a pointed out by Penrose, the fact that the geometry of number density in the unitsity we we are use using. to make Fromthis sense the sense big of ‘special’ the world, as one can part be in traced 10120is. to a perspectivalsystemsphenomenon: aroundpersistent us depends we aspect understand on of the the progress way it betterwe ofinteract asscience. with of the volume of the universe was outsidethe the universe remnants was at small and homogenous to the degree re- bounce to the current epoch the universe has widely ex- due to thethem peculiarity – as the apparent ofThe our hypothesis own motion moving put of forward point the sky of in depends view, [26] is that on the our increase the bounce.the fact If that we assume entropy equiprobability was low inquired the for past by each the [36 equal, current37]. Since standard cosmological model, im- panded. Assuming at least 60 e-folding, the bounce is rather thanown motion.as a globalof entropy feature is a of perspectival all celestial phenomenon objects. in this sense. To volumematter of the was universe, apparently the probability near thermalplies for an a equilibrium observervery ‘special’ to in state the determining an initial low en- not very far from the epoch where the horizon is Planck- III. PAST LOW ENTROPYThe list of conspicuousbe sure, phenomena it is not that subjective have turned or mental, out or illusory. Rather, be outsidepast, the those low remnants entropy at was the concentrated bouncetropy. is one on part the geometry. in This observation opens a novel way for facing the puz- ian, which gives a linear120 expansion factor of the order of to be perspectival isits long; source recognising is in the relation them has between been a an observer system 10 .In Therefore fact, in standard an observer cosmology outside the geometryBut remnants if the is remnant isassumed in scenario to iszle correct, of the the arrow geometry of time: at the universe is in a generic TH and therefore a volume expansion factor of theThe order mystery120 of the second principlepersistent of thermodynam- aspect of theand progress an observed of science. system, like for the rotation of the sky. 3 this sensebe nearly ‘special’ homogenous. as one part in For 10 thethe. gravitational bounce had far field, more ho- volumestate, and was but not su homogenous ciently rich to include subsystems whose of TH .Tohavethesu cient density of remnantsics is todaynot why entropy growth towards the future. That’s This is possible because the entropy of a system de- mogeneity is a very low entropyat configuration, all. To the opposite, because itThe was hypothesiscoupling very highly defines put crumpled. forward a coarse in If [26 graining] is that for the which increase entropy in- to saturate dark matter, we need a density ofpretty the order obvious. The mystery is why entropyof entropy diminishes is a perspectivalpends on phenomenon the system’s in microstate this sense.but To also on the coarse gravity tends to clumpgoing towards and generically theso, what past [ isthe30 the–35 evolution]. origin All current of pastof lowirreversiblecreases entropy, monotonically. ifgraining it is not howunder These which subsystems the system are interacts. those where The relevant 3 III. PAST LOW ENTROPY be sure, it is not subjective or mental, or illusory. Rather, ⇢b ⇢perturbationsT TH leads increasingly(7) special away the from initial homogene- geometry was?informationcoarse can pile graining up and is ‘information determined by gathering the concrete crea- existing ⇠ H ⇠ phenomena, including our own future-orientedits source thinking, is in the relation between an observer system ity. In fact, as longthe existence argued by of Penrose, memories generic and the states direction oftures’ causal- such asinteractions those composing with the the system. biosphere The entropy can exist. we assign to and an observed system, like for the rotation of the sky. at the bounce. Using (4The) we mystery have an of amount the secondity of internal we principle use to make of thermodynam- sense of the world, can be traced to systems around us depends on the way we interact with volume per unit of externalics is not volume why entropy growththe fact towards that entropy the future. was low That’s in the pastThis [36, 37 is]. possible Since becausethem – asthe the entropy apparent of motion a system of the de- sky depends on our IV. PERSPECTIVALpends on the ENTROPY system’s microstate but also on the coarse pretty obvious.2 The mysterymatter is was why apparently entropy diminishes near thermal equilibrium in the own motion. Vintgoing= ⇢bV towardsWH >TH the. pastpast, [30–35 the].(8) low All entropy current was irreversible concentratedgraining on the geometry. under which theThis system observation interacts. opens The a novel relevant way for facing the puz- phenomena, including ourIn fact, own future-oriented in standardAn cosmology imposing thinking, aspects geometrycoarse of the is assumed Cosmos graining to is is the determinedzle mighty of the daily arrow by the of concrete time: the existing universe is in a generic This means that only a fraction the existence of memoriesbe nearly and the homogenous. directionrotation of of For causal- Sun, the gravitational Moon,interactions planets, field, stars with ho- and thestate, allsystem. galaxies but The su ciently entropy rich we to assign include to subsystems whose ity2 we use to120 make sensemogeneity of the world, is aaround very can low be us. traced entropy Why to does configuration,systems the Cosmos around because rotate us so? dependscoupling Well, on it defines theis way a coarsewe interact graining with for which entropy in- 1/TH 10 (9) the fact⇠ that entropy wasgravity low in tends the past tonot clump [ the36, Cosmos37 and]. genericallySince rotating,them the it is evolution – us. as the The apparent of rotationcreases motionof the monotonically. sky of the sky depends These subsystems on our are those where of the volume of the universematter was was outside apparently the remnantsperturbations near thermal at leads equilibriumis a perspectival increasingly in thephenomenon: awayown from motion. homogene- we understandinformation it better as can pile up and ‘information gathering crea- the bounce. If we assumepast, equiprobability the low entropy for wasity. each concentrated In equal fact, asdue longon tothe argued the geometry. peculiarity by Penrose, ofThis our generic own observation states moving point openstures’ of a such novel view, as way those for composing facing the the puz- biosphere can exist. volume of the universe,In the fact, probability in standard for an cosmology observer geometry to rather is assumed than as a to globalzle feature of the of arrow all celestial of time: objects. the universe is in a generic be outside those remnantsbe nearly at the homogenous. bounce is one For part the in gravitationalThe list of field, conspicuous ho- state, phenomena but su that ciently have richturned to out include subsystems whose 10120. Therefore an observermogeneity outside is a very the remnants low entropy is in configuration,to be perspectival because is long;coupling recognising defines them a coarse has graining been a for which entropy in- this sense ‘special’ asgravity one part tends in 10 to120 clump. and genericallypersistent the evolution aspect of of thecreases progress monotonically. of science. These subsystems are those where perturbations leads increasingly away fromThe hypothesis homogene- put forwardinformation in [26 can] is pile that up the and increase ‘information gathering crea- ity. In fact, as long argued by Penrose,of entropy generic is states a perspectivaltures’ phenomenon such as those in this composing sense. To the biosphere can exist. III. PAST LOW ENTROPY be sure, it is not subjective or mental, or illusory. Rather, its source is in the relation between an observer system The mystery of the second principle of thermodynam- and an observed system, like for the rotation of the sky. ics is not why entropy growth towards the future. That’s This is possible because the entropy of a system de- pretty obvious. The mystery is why entropy diminishes pends on the system’s microstate but also on the coarse going towards the past [30–35]. All current irreversible graining under which the system interacts. The relevant phenomena, including our own future-oriented thinking, coarse graining is determined by the concrete existing the existence of memories and the direction of causal- interactions with the system. The entropy we assign to ity we use to make sense of the world, can be traced to systems around us depends on the way we interact with the fact that entropy was low in the past [36, 37]. Since them – as the apparent motion of the sky depends on our matter was apparently near thermal equilibrium in the own motion. past, the low entropy was concentrated on the geometry. This observation opens a novel way for facing the puz- In fact, in standard cosmology geometry is assumed to zle of the arrow of time: the universe is in a generic be nearly homogenous. For the gravitational field, ho- state, but su ciently rich to include subsystems whose mogeneity is a very low entropy configuration, because coupling defines a coarse graining for which entropy in- gravity tends to clump and generically the evolution of creases monotonically. These subsystems are those where perturbations leads increasingly away from homogene- information can pile up and ‘information gathering crea- ity. In fact, as long argued by Penrose, generic states tures’ such as those composing the biosphere can exist. QUANTUM BOUNCE
Quantum Tunneling superposition
Effective repulsive force expanding Planck density solution Size Planck length m 3 24 3 …Vb `P 10 cm ⇠ mP ⇡
Phenomenology signature in the CMB
pre-big-bang accessible
see Ashtekar,Barrau for a review 1504.07559 contracting solution
Quantum Gravity Phenomenology Francesca Vidotto BH EXPLOSION
quantum region
Vidotto, Rovelli 1401.6562 tunnelling
Black -to- White
Quantum Black Holes Francesca Vidotto Scenario 3 FAST EXPLOSION
Quantum Black Holes Francesca Vidotto QUANTUM EFFECTS SHORTEN BH LIFETIME
Black Hole Lifetime Vidotto, Rovelli 1401.6562 Quantum Gravity effects should manifest before the Page time (firewalls!) 3 ⟹ the hole lifetime must be shorter or of the order of ~ m
Black-to-White Tunnelling -1 Minimal time for quantum effects to appear on the horizon: Curvature × (time) ~ (LP) 2 1m ⟹ the hole lifetime must be longer or of the order of ~ m TT 1 mr23 bb ⇠
See also Quantum Break Time Dvali, Gomez 1112.3359
Other BH instabilities? From large extra dimensions? From infinite branes? Gubser 2002, Kol 2002 Emparan, Garcıa-Bellido, Kaloper 2003
Quantum Gravity Phenomenology Francesca Vidotto (QUANTUM) PBH DARK MATTER
Today, black holes smaller than m ( t ) have already exploded. |t=tH It decreases with time. ( but for later accretion/merging )
Caution with constraints! Raccanelli, Vidotto, Verde 1708.02588
1 A 8 B Constraints from +BCA B B Hawking evaporation 04 do not apply any more. G 2,0 Effects on late cosmology 9 G
Galaxy clusters surveys G 3/ BCA6 CB DBC8A 45 8 B 2A8 DB BCA6 CB
G G G G G G 1 1H
Quantum Gravity Phenomenology Francesca Vidotto 3 where refers to the overdensity in the comoving gauge, magnified and become detectable, so that the observed rsd and v denote Doppler effects and peculiar velocity number density of sources increases. At the same time, [49], the lensing convergence and pot incorporates lo- the stretching of the field of view leads to a decrease of cal and non local terms depending on Bardeen potentials the observed number density. The combined effect can and their temporal derivatives; t includes tensor pertur- be written as: bation effects. For simplicity, we omitted the redshift and nobs(z)=n (z)[1 + (5s 2)] , (6) direction dependencies (n,z). g Galaxy clustering measurements have been used to obs where n and ng are the observed and intrinsic number measure cosmological parameters for a variety of cosmo- of sources, respectively, s is the magnification bias and logical models (see e.g. [50–56]), and it is the focus of is the convergence. The net modification of the observed many future large scale galaxy surveys (see e.g. [57–61]). number density is called magnification bias s: Therefore it is interesting to see that it can also be used to test different QG models and potentially extend con- d logN a`m `m(n), with `m denoting the spherical harmon- 2 2 Y perturbedY by peculiar velocities, ics functions, n the direction on the sky and zi is the red- cross-correlating galaxies in two disjoint redshift bins (see P gravitational lensing and potentials e.g. [69, 70]).0, ,4 1 shift. This can be calculated from the underlying matter 0, ,4 1 6 power spectrum by using: 0, ,4 1 4⇡dk C. Galaxy surveys CXY (z ,z )= 2(k) W X(k, z ) W Y(k, z ) , (4) ` i j k ` i ` j Z We model our galaxy 6 6 survey after the Square Kilo- X,YChoice of redshift distribution: 2 where W`{ } are the source distribution kernels for the metre Array (SKA) , which is an international multi- 7 different observables (i.e. galaxies in different redshift purpose next-generation radio interferometer, that will 1.+ 265 35884 0 bins) and 2(k) )is the dimensionless matter power spec- be built in the Southern Hemisphere in Africa and in 2 trum today. Australia,88 with a total collecting area of about 1 km . , 7 The kernel for the galaxy clustering can be written as Among many , 0 types of observations delivered by such in- (see e.g. [62]): struments,2 1 we focus 5 3 here1 on surveys that will detect in- 2 1 5 3 dividual galaxies in the radio1 continuum [71]; we assume ( 7 2 X dN X (z) 2 1 5 31 ) that the survey will cover 30, 000 deg ,andwecompute W` (k)= D(z) bX(z) j`[k (z)] dz , (5) dz results for a flux limit of 1µJy .Althoughradiocontin- Z uum surveys do not have in principle redshift informa- where dN (z)/dz is the objects redshift distribution, QuantumX Gravity Phenomenology tion, some techniques haveFrancesca been Vidotto proposed to allow the D(z) the growth rate of structures, b (z) is the bias X possibility to divide the galaxy catalog into tomographic that relates the observed overdensity to the underlying redshift bins; here we follow the clustering-based redshift matter distribution (see [63] for a recent review); j (x) ` (CBR) information approach proposed in [72], and stud- is the spherical Bessel function of order `,and (z) is ied for some cosmological applications (including some the comoving distance. predictions for the SKA), in [73]. In Figure 1 we show the (normalized) redshift distribution for the SKA radio continuum survey we use for this paper. We compute the observational consequences of BH de- B. Cosmic Magnification cay by using a modified version of the class3 code, and we investigate the effects on galaxy angular power spec- Gravitational lensing causes the deflection of light rays tra. Given the specifications of the proposed future sur- by the matter distribution along the line of sight, causing veys, we forecast the measurements’ precision using the two competing effects: on one hand, a size magnification of sources behind a lens, on the other hand lensing causes the stretching of the observed field of view. Therefore, for magnitude (or flux) limited galaxy surveys, sources 2 https://skatelescope.org that are just below the threshold for detection will be 3 http://class-code.net/ Characterisation of the signal Quantum Black Holes Francesca Vidotto PBH EXPLOSIONS Barrau, Rovelli, Vidotto 1409.4031 fast process ( few milliseconds? ) the source disappears with the burst very compact object: big flux E = mc2 1.7 1047 erg ⇠ ⇥ tH 2Gm exploding today: m = 1.2 1023 kg R = 2 .02 cm r 4k ⇠ ⇥ c ⇠ 2Gm LOW ENERGY: size of the source ≈ wavelengthR = predicted & . 02 . 05 cm cm (?) c2 ⇠ HIGH ENERGY: energy of the particle liberated Tev ⇡ SYNCHROTRON EMISSION Kavic &al. 0801.4023 GRAVITATIONAL WAVES Quantum Gravity Phenomenology Francesca Vidotto FAST RADIO BURSTS fast process ( few milliseconds ) compact object: big flux E = mc2 1.7 1047 erg ⇠ ⇥ HIGH ENERGY Tev ➞ REES’ MECHANISM Kavic &al. 0801.4023 ⇡ Electron-positron pairs traveling trough a magnetic field Repetition can be due to: • reflection of the signal due to plasm walls • region dense of PBH 2Gm LOW ENERGY: size of the source ≈ wavelength R = . 02. 05 cm cm predictedc2 ⇠& We may have missed a factor in our rough calculation! We may be seeing only the a window in a distribution of event Barrau &al. 1801.03841 Quantum Gravity Phenomenology Francesca Vidotto MAXIMAL DISTANCE Barrau, Bolliet, Vidotto, Weimer 1507.1198 shorter lifetime — smaller wavelength Low energy channel High energy channel 1024 1028 1022 26 Hubble radius 10 Galactic scale ] ] 1020 m m 24 [ 10 [ R R Hadron decay 1018 1022 Galactic scale Direct emission 1016 1020 k 1 104 108 1012 1016 1020 k 1 104 108 1012 1016 1020 E [eV] 2.7 2.7×102 2.7×104 2.7×106 2.7×108 E [eV] 3.6×1013 3.6×1014 3.6×1015 3.6×1016 3.6×1017 detection of arbitrarily far signals PBH: mass - temperature relation better single-event detection different scaling Quantum Gravity Phenomenology Francesca Vidotto THE SMOKING GUN: DISTANCE/ENERGY RELATION distant signals originated in younger, smaller&hotter sources Quantum Gravity Phenomenology Francesca Vidotto THE SMOKING GUN: DISTANCE/ENERGY RELATION distant signals originated in younger, smaller&hotter sources Quantum Gravity Phenomenology Francesca Vidotto THE SMOKING GUN: DISTANCE/ENERGY4 RELATION by 1 1/2 other other 2Gm H0 1 ⌦⇤ =(1+z) . (6) 3/2 obs emitted obs 2 (1 + z) 1/2 sinh (z + 1) ⟶ ⇠ c v ⌦M u6 k⌦⇤ " # u ✓ ◆ The specific redshift dependence of our model makes t it possibly testable against other proposals. Obvi- 2 ously, detecting such a signal from far away galaxies is challenging but this work might precisely motivate some experimental prospects for the next generation ofl gamma-ray satellites. distance ∝ 1/wave length noise. There might be room for improvement. It is not The order of magnitude of the number of bouncing impossible that the time structure of the bounce could black holes in the galactic center region required to ac- count for the observed taking flux into is 100 account per second. the The asso- lead to a characteristic time-scale of the event larger than ciated mass is negligible when compared to the expected dark matter density,redshift even the when resulting integrated function over a long the response time of the bolometer. In that case, a time interval. If theis very mass slowly spectrum varying of primordial black FIG. 3. Best fit to the Fermi excess with bouncing black holes was known, which is not the case, it would in prin- specific analysis should allow for a dedicated search of holes. ciple be possible to fix the total mass associated with bouncing black holes. As a reasonable toy model, let us such events. We leave this study for a future work as assume that the mass spectrum is given by it requires astrophysical considerations beyond this first DISCRIMINATION WITH DARK MATTER AND Barrau,2 Rovelli, Vidotto 1409.4031 z d N ↵ 2 4 6 8 10 MASS SPECTRUM = pM . (7) dMdV investigation. An isotropic angular distribution of the Quantum Gravity Phenomenology Francesca Vidotto The model presented in this work is unquestionably If the number of exploding black holes required to explain bursts, signifying their cosmological origin, could also be quite exotic when compared to astrophysical hypotheses. the data on a time intervalFIG.d⌧ is Nexp 1:, one White can estimate hole signal wavelength (unspecified units) as But the important point is than it can, in principle, be the mass variation associated, considered as an evidence for the model. In case many distinguished both from astrophysical explanations and a function of z. Notice the characteristic flattening at large d⌧ from other “beyond the standard model” scenarios. The dM = . (8) distance:8kM the youth of the hole compensate for the redshift. events were measured, it would be important to ensure reason for that is the redshift dependance. When look- ing at a galaxy at redshift z, the measured energy of With M0 the mass corresponding to a black hole explod- that there is no correlation with the mean cosmic-ray flux the signal emitted either by decaying WIMPS or by as- ing now, one then has trophysical objects will be E/(1 + z) if the rest-frame (varying with the solar activity) at the satellite location. energy is E. But this is not true for the bouncing black M0+dM N = pM ↵dM. (9) holes signal. The reason for this is that black holes that exp The received signal is going to be corrected by standard M0 Let us turn to something that has been observed. have bounced far away and are observed now must have Z a smaller bouncing time and therefore a smaller mass. This allows, in principe, tocosmological determine p and therefore redshift. to However, signals coming form far- Fast Radio Bursts. Fast Radio Bursts are intense iso- Their emission energy – in the low energy channel we are normalize the spectrum. considering in this article – is therefore higher and this ther away were originated earlier, namely by younger, lated astrophysical radio signals with milliseconds dura- partly compensates for the redshift e↵ect. Following [9], we can write down the observed wavelength of the signal CONCLUSIONand therefore less massive, holes, giving a peculiar de- tion. A small number of these were initially detected from a host galaxy at redshift z, taking into account both the expansion of the universe and the change of bouncing Black holes could bouncecrease once they have of reached the the emitted wavelength with distance. The re- only at the Parkes radio telescope [39–41]. Observations time, as: “Planck star” stage. This is a well motivated quantum gravity idea. In this article,ceived we have shown wavelength, that this taking into account both the expan- 2Gm phenomenon could explain the GeV excess measured by from the Arecibo Observatory have confirmed the detec- BH (1 + z) (5) obs ⇠ c2 ⇥ the Fermi satellite. This wouldsion open of the fascinating the universe pos- and the change of time available for tion [42]. The frequency of these signals around 1.3 GHz, 1 1/2 sibility to observe (non perturbative) quantum gravity H0 1 ⌦⇤ 3/2 processes at energies 19 ordersthe of black magnitude hole below the to bounce, can be obtained folding (1)into 1/2 sinh (z + 1) , v ⌦M namely a wavelength u6 k⌦⇤ " # Planck scale. Interestingly the explanation we suggest is u ✓ ◆ t fully self consistant in the sensethe that standard the hadronic “noise” cosmological relation between redshift and where we have reinserted the Newton constant G and due to decaying pions remains much below the observed the speed of light c; H0, ⌦⇤ and ⌦M being the Hubble background. Unquestionably,proper there are other time. – less exotic A straightforward calculation gives constant, the cosmological constant, and the matter den- – ways to explain the Fermi excess. But the important observed 20 cm. (7) sity. On the other hand, for other signals the measured point we have made is that there is specific redshift de- ⇠ wavelength this just related to the observed wavelength pendance of this model which, in principle, can2 leadGm to a obs (1 + z) (6) These signals are believed to be of extragalactic origin, ⇠ c2 ⇥ because the observed delay of the signal arrival time with 1 1/2 H0 1 ⌦⇤ frequency agrees well with the dispersion due to ionized sinh (z + 1) 3/2 . 1/2 medium as expected from a distant source. The total v ⌦M u6 k⌦⇤ " # u ✓ ◆ energy emitted in the radio is estimated to be of the t 38 where we have reinserted the Newton constant G and order 10 erg. The progenitors and physical nature of the Fast Radio Bursts are currently unknown [42]. the speed of light c while H0, ⌦⇤ and ⌦M are the Hub- ble constant, the cosmological constant, and the matter There are three orders of magnitude between the pre- density. This is a very slowly varying function of the dicted signal (5) and the observed signal (7). But the redshift. The e↵ect of the hole’s age almost compesates black-to-white hole transition model is still very rough. It for the red-shift. The signal, indeed, varies by less than disregards rotation, dissipative phenomena, anisotropies, an order of magnitude for redshifts up to the decoupling and other phenomena, and these could account for the time (z=1100). See Figure 1. discrepancy. If the redshift of the source can be estimated by using In particular, astrophysical black holes rotate: one may dispersion measures or by identifying a host galaxy, given expect the centrifugal force to lower the attraction and su cient statistics this flattening represents a decisive bring the lifetime of the hole down. This should allow signature of the phenomenon we are describing. larger black holes to explode today, and signals of larger Do we have experiments searching for these signals? wavelength. Also, we have not taken the astrophysics of There are detectors operating at such wavelengths, begin- the explosion into account. The total energy (3) avail- ning by the recently launched Herschel instrument. The able in the black hole is largely su cient –9 orders of 200 micron range can be observed both by PACS (two magnitude larger– than the total energy emitted in the bolometer arrays and two Ge:Ga photoconductor arrays) radio estimated by the astronomers. and SPIRE (a camera associated with a low to medium Given these uncertainties, the hypothesis that Fast Ra- resolution spectrometer). The predicted signal falls in be- dio Burst could originate from exploding white holes is tween PACS and SPIRE sensitivity zones. There is also a tempting and deserves to be explored. very high resolution heterodyne spectrometer, HIFI, on- High energy signal. When a black hole radiates by board Herschel, but this is not an imaging instrument, it the Hawking mechanism, its Schwarzschild radius is the observes a single pixel on the sky at a time. However, the only scale in the problem and the emitted radiation has bolometer technology makes detecting short white-hole a typical wavelength of this size. In the model we are bursts di cult. Cosmic rays cross the detectors very of- considering, the emitted particles do not come from the ten and induce glitches that are removed from the data. coupling of the event horizon with the vacuum quan- Were physical IR bursts due to bouncing black hole regis- tum fluctuations, but rather from the time-reversal of tered by the instrument, they would most probably have the phenomenon that formed (and filled) the black hole. been flagged and deleted, mimicking a mere cosmic ray Therefore the emitted signal is characterized by second 1 1 4 1 1 2 1 4 meas 2⇡ (1 + z) H0 1 ⌦⇤ 1 3 2 meas 2⇡ (1 + z) H0 1 2⌦⇤ 3 high 1 1 1/2 sinh sinh(1 + z) . (1 + z) 2 . (6) (6) ⇠ kBT (0.3g high) 2 1 1 ⌦M 1/2 ⇠"6kkB⌦T⇤ (0.3g ) 2""6k⌦ " ⌦##M ## ⇤ ⇤ ✓ ⇤◆ ✓ ◆ This shows that althoughThis shows the that mean although wavelength the mean does wavelengthIt is worth does consideringIt is worth the consideringn(R) term the a bitn(R more) term in a bit more in decreases as a functiondecreases of k asin a both function cases, of itk doesin both not cases,detail. it does If not one denotesdetail. by If onedn denotesthe initial by dn di↵erentialthe initial di↵erential 1 1 dMdV dMdV follow the same generalfollow behavior. the same general It scales behavior. with k It2 scalesmass with spectrumk 2 ofmass primordial spectrum black of primordial holes per unit black volume, holes per unit volume, 1 1 for the low energyfor component the low energy and as componentk 4 for the and high as k 4itfor is possible the high to defineit is possiblen(R) as: to define n(R) as: energy one. energy one. M(t+ t) M(t+ t) dn n(R)=dn dM, (8) The following conclusionsThe following can be conclusions drawn: can be drawn: n(R)= dM, dMdV(8) M(t) dMdVZM(t) The low energy channel leads to a better single- Z The low energy channel• leads to a better single- • event detection thanevent the detectionhigh energy than thechannel.high energyleadingchannel. to leading to Although lower energy dilutes the signal in a Although lower energy dilutes the signal in a dn t higher astrophysicalhigher background, astrophysical this e↵ background,ect is over- this e↵ect is over- dn n(tR) , (9) n(R) , ⇡ dMdV 8k (9) compensated by thecompensated larger amount by the of photons. larger amount of photons. ⇡ dMdV 8k The di↵erence of maximal distances between the where the mass spectrum is evaluated for the mass cor- The di↵erence of maximal distances between the where the mass spectrum is evaluated for the mass cor- • low- and high energy channels decreases for higher responding to a time (t R ). If one assumes that pri- • low- and highINTEGRATED energy channels decreasesEMISSION for higher responding to a time (t R ). If one assumesH c that pri- values of k, i.e. for longer black-hole lifetimes. H c Barrau, Bolliet,mordial Vidotto, black Weimer holes1507.1198 are directly formed by the collapse values of k, i.e. for longer black-hole lifetimes. mordial black holesof density are directly fluctuations formed with by athe high-enough collapse density con- In the low energy channel,⌧ form the2 smallerof density values fluctuations with a high-enough density con- In the low energy• channel, for the smaller values⇠ trast in the early Universe, the initial mass spectrum is • of k, a single bounce can be detectedtrast arbitrary in the far earlydirectly Universe, related the toinitial the equation mass spectrum of state is of the Universe of k, a single bounceaway can in be the detected Universe. arbitrary far directly related to the equation of state of the Universe away in theLow Universe. energy channel High energy channelat the formation epoch. It is given by [18, 19]: k=0.05 In all cases, the distances are large enoughat the and formation ex-direct epoch. It is given bydecayed [18, 19]: • dn 1+3w In all cases, the distancesperimental are large detection enough is far and from ex- being hopeless. 1 1+w • 1+3w = ↵M , (10) k=0.05 k=100 dn 1dMdV perimental detection is far from being hopeless. = ↵M 1+w , (10) dMdV III. INTEGRATED EMISSION where w = p/⇢. In a matter-dominated universe the 1+3w III. INTEGRATED EMISSION where w = p/⇢.exponent In a matter-dominated 1 1+w takes universe the the value = 5/2. direct+decayed The normalization1+3w ⌘ enlarged coe cient ↵ will be kept unknown In addition to the instantaneous spectrumexponent emitted by a 1 1+w takes the value = 5/2. ⌘ as it depends on the details of the black hole formation single bouncing black hole, it is interesting toThe consider normalization the coe cient ↵ will be kept unknown In addition to the instantaneous spectrum emitted by a mechanism. For a sizeable amount of primordial black as it depends9 on the details of the black hole formation single bouncing blackpossible hole, it di is↵ interestinguse background tok=10000 consider due to the the integratedk=10 emis- mechanism. Forholes a sizeable to form, amount the power of primordial spectrum black normalized on the possible di↵use backgroundsion of a duepopulation to the of integrated bouncing emis- black holes. Formally, holes to form, theCMB power needs spectrum to be boosted normalized at small on the scales. This can sion of a populationthe of number bouncing of measured black holes. photons Formally, detected per unit time, CMB needs to bebe achieved,boosted at for small example, scales. through This Staobinsky’s can broken the number of measuredunit energy photons and detected unit surface, per unit can time, be written as: be achieved, forscale example, invariance through (BSI) Staobinsky’s scenario. broken The idea is that the unit energy and unit surface, can be written as: dNmes scale invariancemass (BSI) spectrum scenario. takes The a high idea enough is that value the in the relevant = ind((1+z)E,R) n(R) Acc Abs(E,Rcharacteristic)dR, shape: distorted black body dN dEdtdS · · · mass spectrum takesrange a whereas high enough it is naturally value in the suppressed relevant at small masses mes Z by inflation and at large masses by the BSI hypothesis. = ind((1+z)E,R) n(R) Acc Abs(E,R)dR, range whereas(7) it is naturally suppressed at small masses dEdtdS where (·E,R)· denotes· the individual flux emitteddepends on howWe much will not DM study are PBL those questions here and just consider Z ind (7) by inflation and at large masses by the BSI hypothesis. by a single bouncing black hole at distance R and at the shape of the resulting emission, nor its normalisation We will not study those questions here and just consider where ind(E,R) denotesenergy E the, Acc individualis the angular flux acceptance emitted of the detector which depends sensitively on the bounds of the mass by a single bouncingQuantummultiplied black Gravity hole Phenomenology by its at e distance ciencyR (inand principle at thisthe shape is also of a the resultingspectrum, emission, thatFrancesca are Vidotto highly nor its model-dependent. normalisation As this part energy E, Acc is thefunction angular of acceptanceE but this of will the be detector ignored here),whichAbs( dependsE,R) sensitivelyof the study on is thedevoted bounds to the of investigation the mass of the shape multiplied by its eis ciency the absorption (in principle function, this and is alson(R) a is thespectrum, number that of areof highlythe signal, model-dependent. the y axis on the As figures this part are not normalized. function of E but thisblack will holes be bouncingignored here), at distanceAbs(E,RR per) unitof the time study and is devoted to the investigation of the shape is the absorption function,volume. and Then distance(R) is theR numberand the of redshiftof thez entering signal, the y axisFortunately, on the figures the results are not are normalized. weakly dependent upon black holes bouncingthe at above distance formulaR per are unit linked. time The and integration has to the shape of the mass spectrum. This is illustrated in volume. The distancebe carriedR and out the up redshift to cosmologicalz entering distancesFortunately, and it is theFig. results 5 where are di↵ weaklyerent hypothesis dependent for upon the exponent are the above formulatherefore are linked. necessary The integration to use exact has results to behindthe the shape linear of thedisplayed. mass spectrum. The resulting This is electromagnetic illustrated in spectrum is be carried out upapproximation. to cosmological The distances energy and is also it is correlatedFig. 5 with whereR di↵erentalmost hypothesis exactly the for same. the exponent Therefore are we only keep one therefore necessaryas to theuse exactdistance results fixes behind the bounce the linear time of thedisplayed. black hole Thecase resulting ( = electromagnetic5/2, corresponding spectrum to w =1 is/3). The black approximation. Thewhich, energy subsequently, is also correlated fixes the emitted with R energy.almost exactly theholes same. are assumed Therefore to we be only uniformly keep onedistributed in the as the distance fixes the bounce time of the black hole case ( = 5/2,Universe, corresponding which to isw a=1 meaningful/3). The hypothesis black as long as which, subsequently, fixes the emitted energy. holes are assumed to be uniformly distributed in the Universe, which5 is a meaningful hypothesis as long as 5 1 1 4 1 2 meas 2⇡ (1 + z) H0 1 ⌦⇤ 3 2 high 1 1 1/2 sinh (1 + z) . (6) ⇠ kBT (0.3g ) 2 "6k⌦ " ⌦M ## ⇤ ⇤ ✓ ◆ This shows that although the mean wavelength does It is worth considering the n(R) term a bit more in decreases as a function of k in both cases, it does not detail. If one denotes by dn the initial di↵erential 1 dMdV follow the same general behavior. It scales with k 2 mass spectrum of primordial black holes per unit volume, 1 for the low energy component and as k 4 for the high it is possible to define n(R) as: energy one. 1 M(t+ t) 1 4 dn 1 2 measThe following2⇡ (1 + conclusionsz) H0 can be drawn:1 ⌦⇤ 3 n(R)= dM, (8) 2 high 1 1 1/2 sinh (1 + z) . M((6)t) dMdV ⇠ kBT (0.3g ) 2 "6k⌦ " ⌦M ## Z The low energy⇤ channel⇤ leads to✓ a better◆ single- • event detection than the high energy channel. leading to Although lower energy dilutes the signal in a 1 1 4 dn t 1 higher astrophysical2 background, this e↵ect is over- meas This2⇡ shows(1 + thatz) althoughH0 the1 mean⌦ wavelength⇤ does3 It is worth considering the n(R) term a bitn more(R) in , (9) 2 high 1 1 1/2 sinh compensated(1 by + z the) larger. amount of photons. (6) dn ⇡ dMdV 8k decreases⇠ k T as a function2 of k in both⌦ cases, it does not detail. If one denotes by the initial di↵erential B (0.3g ) "6k⌦ " M 1## dMdV ⇤ ⇤ ✓ ◆ follow the same general behavior. It scales with k 2 mass spectrum of primordial black holes per unit volume, The di↵erence1 of maximal distances between the where the mass spectrum is evaluated for the mass cor- for the low energy component• and as k 4 for the high it is possible to define n(R) as: R low- and high energy channels decreases for higher responding to a time (tH c ). If one assumes that pri- energy one. values of k, i.e. for longer black-hole lifetimes. mordial black holes are directly formed by the collapse M(t+ t) This shows that although the mean wavelength does It is worth considering the n(R) term a bit more in of densitydn fluctuations with a high-enough density con- dn n(R)= dM, (8) decreases as a function of k in bothThe following cases, it doesconclusions not candetail. beIn drawn: the If onelowPBH denotes energy MASSchannel, by SPECTRUM forthe the initial smaller di↵erential values trastdMdV in the early Universe, the initial mass spectrum is 1 • PBH MASSdMdV SPECTRUM M(t) follow the same general behavior. It scales with k 2 massof spectrumk, a single of primordialbounce can black be detected holes per arbitrary unit volume,Z far The low1 energy channel leads to a better single- directly related to the equation of state of the Universe 4 away in the Universe. for the low energy component and• aseventk detectionfor the high thanit the is possiblehigh energy to definechannel.n(R) as:leading to at the formation epoch. It is given by [18, 19]: energy one. Although lower energy dilutes the signal in a In all cases, the distancesM(t+ t are) large enough and ex- higher astrophysical background,• this e↵ect is over- dn dn t dn 1 1+3w perimentaln( detectionR)= is far from beingdM, hopeless.n(R(8)) , =(9)↵M 1+w , (10) The following conclusions can be drawn:compensated by the larger amount of photons. dMdV ⇡ dMdV 8k dMdV ZM(t) The low energy channel leads to a better single- • The di↵erence of maximalleading distances toIII. betweenINTEGRATED the where EMISSION the mass spectrum iswhere evaluatedw = forp/ the⇢. mass In a cor- matter-dominated universe the event detection than the high• energy channel. Low energy channel R 1+3w low- and high energy channels decreases for higher responding to a time (tH exponent). If one assumes1 that pri- takes the value = 5/2. Although lower energy dilutes the signal in a c 1+w values of k, i.e. for longer black-hole lifetimes. mordial black holes are directlyThe formed normalization by⌘ the coecollapse cient ↵ will be kept unknown higher astrophysical background, this e↵ect is over- In addition to the instantaneousdn spectrum t emitted by a n(R) of density, fluctuations(9) withas a high-enough it depends on density the details con- of the black hole formation compensated by the larger amount of photons.1 ⇡ dMdV 8k behavior. It scalesIn the withlowk 2 energyfor thechannel, lowsingle energy bouncing for compo- the smaller black hole, values it is interesting to consider the • 1 trast in the early Universe, themechanism. initial mass For spectrum a sizeable is amount of primordial black nent and as k of4 fork, a the single high bounce energy one.The canpossible be detected following di↵use arbitrarybackground far due to the integrated emis- The di↵erence of maximal distances between the where the mass spectrum is evaluateddirectly for related the mass to the cor- equationholes of to state form, of theDifferent the Universe power mass spectrum spectra normalized on the • conclusions canaway be drawn: in the Universe.sion of a population of bouncingR black holes. Formally, low- and high energy channels decreases for higher responding to a time (t ).at If the one formation assumes that epoch. pri- It isCMB given needs by [18, to 19]:gives be boosted qualitatively at small same scales. This can the number of measured photonsH c detected per unit time, values of k, i.e. for longerThe black-holelow energyIn all cases, lifetimes.channel the leads distances to amordial better are large single- black enough holes and are ex- directly formed by the collapse be achieved, for example,diffuse emission… through Staobinsky’s broken • • unit energy and unit surface, can be written as: 1+3w event detectionperimental than the detectionhigh energy is farofchannel. density from being fluctuations Al- hopeless. with a high-enough densitydn con- scale1 invariance (BSI) scenario. The idea is that the In the low energy channel, for the smaller values = ↵M 1+w , (10) though a lower energy dilutes thedNtrast signal in the in early a Universe, the initial mass spectrumdMdV is mass spectrum takes a high enough value in the relevant • of k, a single bounce can be detected arbitrary far mes higher astrophysical background, thisdirectly e↵ect= is related over- ind to((1+ thez equation)E,R) n( ofR) stateAcc ofAbs the(E,R Universe)dR, range whereas it is naturally suppressed at small masses away in the Universe. dEdtdS · · · compensated byIII. the larger INTEGRATED amountat of photons.the EMISSION formationZ epoch. It is givenwhere byw [18,= 19]:p/⇢. In(7) a matter-dominatedby inflation and universe at large the masses by the BSI hypothesis. exponent 1 1+3w takes the value = 5/2. In all cases, the distancesThe are di↵erence large enough of maximal and ex- distanceswhere between ind(E,R the ) denotes the individual flux⌘ emitted 1+w We will not study those questions here and just consider • The1+3 normalizationw coe cient ↵ will be kept unknown perimental detection• is far fromIn addition being hopeless. to the instantaneousby a single spectrum bouncing emitteddn black by a hole1 at distance R and at the shape of the resulting emission, nor its normalisation low- and high energy channels decreases for higher = ↵M as it1+ dependsw , on the(10) details of the black hole formation single bouncing black hole, itenergy is interestingE, Acc tois consider thedMdV angular the acceptance of the detector which depends sensitively on the bounds of the mass values of k, i.e. for longer black-hole lifetimes. mechanism. For a sizeable amount of primordial black possible di↵use backgroundmultiplied due to the by integrated its e ciency emis- (in principle this is also a spectrum, that are highly model-dependent. As this part holes to form, the power spectrum normalized on the III. INTEGRATEDIn thesion EMISSIONlow of energya populationchannel, of for bouncing thefunctionwhere smaller blackw of values=E holes.butp/⇢. this Formally, In will a matter-dominated be ignored here), universeAbs(E,R the) of the study is devoted to the investigation of the shape • of k, a single bounce can be detected arbitrary far 1+3w CMB needs to be boosted at small scales. This can the number of measured photonsisexponent the detected absorption per function, unit1 time,1+w andtakesn(R the) is value the number = 5 of/2. of the signal, the y axis on the figures are not normalized. away in the Universe. The normalization⌘ FIG. coe 5: cientLow energy↵bewill achieved,channel be kept forsignal unknown example, calculated through for di↵erent Staobinsky’s broken In addition to the instantaneousunit spectrum energy and emitted unit by surface, a black can holesbe written bouncingQuantum as: atGravity distance PhenomenologyR per unit time and Francesca Vidotto as it depends on themass details spectra. ofscale As the the black invariance mass hole spectrum formation (BSI) is not scenario. normalized, The the idea is that the single bouncing black hole, itIn is all interesting cases, the to distances consider are the largevolume. enough and The ex- distanceunits ofR theandy axis the are redshift arbitrary.z entering Fortunately, the results are weakly dependent upon dNmes mechanism. For a sizeable amountmass spectrum of primordial takes black a high enough value in the relevant possible di↵use background• perimental due to the detection= integrated is((1+ far emis- fromz)E,R beingthe) aboven hopeless.(R) Acc formulaAbs(E,R are) linked.dR, The integration has to the shape of the mass spectrum. This is illustrated in ind holes to form, the power spectrumrange whereas normalized it is on naturally the suppressed at small masses sion of a population of bouncingdEdtdS black holes. Formally, be carried· · out· up to cosmological distances and it is Fig. 5 where di↵erent hypothesis for the exponent are Z CMB needs to be boosted(7) atby small inflation scales. and This at large can masses by the BSI hypothesis. the number of measured photons detected per unit time, therefore necessary towhere use the exact mass results spectrum behind is evaluated the linear for thedisplayed. mass cor- The resulting electromagnetic spectrum is whereIII. INTEGRATED ind(E,R) denotes EMISSION thebe individual achieved, for flux example, emitted throughWe will Staobinsky’s not studyR thosebroken questions here and just consider unit energy and unit surface, can be written as: approximation. Theresponding energy is to also a time correlated (tH ). with TheR shapealmost of the mass exactly the same. Therefore we only keep one by a single bouncing black holescale at invariance distance (BSI)R and scenario. at the The shape idea of the isc resulting that the emission, nor its normalisation as the distance fixesspectrum the bounce obviously time depends of the black on the hole detailscase of the ( for-= 5/2, corresponding to w =1/3). The black dN energy E, Acc is the angularmass acceptance spectrum of the takes detector a high enoughwhich value depends in the sensitively relevant on the bounds of the mass mes In addition to the instantaneous spectrumwhich, emitted subsequently, by a mation fixes the mechanism emitted (see energy. [39] for a review onholes PBHs are and assumed to be uniformly distributed in the = ind((1+z)E,R)multipliedn(R) Acc byAbs its(E,R e )ciencydR, (inrange principle whereas this it is is naturally also a suppressedspectrum, at that small are masses highly model-dependent. As this part dEdtdS single bouncing· black· · hole, it is interesting to consider the inflation). As an example, we shall assume thatUniverse, primor- which is a meaningful hypothesis as long as Z possible difunction↵use background of E but due this to(7) will the be integratedby ignored inflation emis- here), andAbs atdial large(E,R black masses) holesof by the are the study directly BSI is hypothesis. formed devoted by to the the collapse investigation of of the shape where ind(E,R) denotession of the ais population individual the absorption of flux bouncing emitted function, black and holes.Wen will( Formally,R) not is studythe numberdensity those questions of fluctuationsof the here with signal, and a high-enoughjust the y consideraxis on density the figures contrast are not normalized. by a single bouncingthe black number holeblack of at measured holesdistance bouncing photonsR and detectedat at distancethe per shape unitR per time, of unit the resulting timein the and early emission, Universe. nor The its normalisation initial mass spectrum5 is then energy E, Acc is the angularunit energy acceptancevolume. and unit The of surface, the distance detector can beR writtenandwhich the as: depends redshift sensitivelyz directlyentering related on the toFortunately, bounds the equation of the the of state results mass of arethe Universe weakly dependent upon multiplied by its e ciency (inthe principle above formula this is also are linked. a spectrum, The integration that areat highly has the formation to model-dependent.the epoch. shape It of is As the given this mass by part [33, spectrum. 40]: This is illustrated in dNmes function of E but this will be=be ignored carried ind here),((1+ outz)AbsE,R up()E,R ton( cosmologicalR)) A(ofE) thef(E,R study distances)dR, is devoted and it to is the investigationFig. 5 where of di↵ theerent shape hypothesis for the exponent are dEdtdS · · · dn 1 1+3w is the absorption function, andthereforen(R) is necessary the number to use of exactof the results signal, behind the y theaxis linear on the figuresdisplayed. are not= ↵ TheM normalized. resulting 1+w , electromagnetic(14) spectrum is Z (11) dMdV black holes bouncing at distanceapproximation.R per unit time The and energy is also correlated with R almost exactly the same. Therefore we only keep one where ind(E,R) denotes the individual flux emitted volume. The distancebyR a singleandas the bouncingthe redshift distance blackz fixesentering hole the at bounce distanceFortunately, timeR and of at the the blackwhere results holew = arep/case weakly⇢. In( a= dependent matter-dominated5/2, corresponding upon universe to w the=1/3). The black 1+3 w the above formula are linked.which, The integration subsequently, has fixes to thethe emitted shape energy. of the massexponent spectrum. holes1 This are is assumed illustratedtakes the to value inbe uniformly = 5/2. distributed in the energy E, A(E) is the angular acceptance of the detector ⌘ 1+w be carried out up tomultiplied cosmological by its distances e ciency, andf(E,R it is) isFig. the absorption 5 where di↵erentThe hypothesis normalizationUniverse, for coe the exponent whichcient ↵ iswill a meaningfulare be kept unknown hypothesis as long as therefore necessary tofunction, use exact and resultsn(R) behind is the number the linear of blackdisplayed. holes bouncing The resultingas it depends electromagnetic on the details spectrum of the black is hole formation approximation. Theat energy distance is alsoR per correlated unit time with and volume.R almost The distance exactly themechanism. same. Therefore For a sizeable we only amount keep of one primordial black 5 as the distance fixes theR and bounce the timeredshift of thez entering black hole the abovecase formula ( = are5/2, correspondingholes to form, to thew power=1/3). spectrum The black normalized on the CMB needs to be boosted at small scales. The formula which, subsequently, fixeslinked. the emitted The integration energy. has to be carriedholes out are up assumed to to be uniformly distributed in the given above might therefore be correct only within a cosmological distances and it is thereforeUniverse, necessary which to is a meaningful hypothesis as long as use exact results behind the linear approximation. The limited interval of masses. The idea is that the mass energy is also correlated with R as the distance fixes the spectrum takes a high enough value in the relevant bounce time of the black hole which, subsequently,5 fixes range whereas it is naturally suppressed at small masses the emitted energy. by inflation. We will neither study those questions here (focusing on the shape of the resulting emission), It is worth considering the n(R) term a bit more into nor the normalisation issues which depend sensitively dn on the bounds of the mass spectrum, that are highly the details. If one denotes by dMdV the initial di↵erential mass spectrum of primordial black holes per unit volume, model-dependent. As this part of the study is devoted it is possible to define n(R) as: to the investigation of the shape of the signal, the y axis on the figures are not normalized. As we show M(t+ t) dn below, the shape of the signal is quite independent on n(R)= dM, (12) the shape of the mass spectrum, so Eq. 14 does not play dMdV ZM(t) any significant role for the spectra computer. leading to The results are indeed very weakly dependent upon dn t the shape of the mass spectrum. This is illustrated in n(R) , (13) ⇡ dMdV 8k Fig. 5 where di↵erent hypothesis for the exponent are 6 to conclude Quantum Black Holes Francesca Vidotto SUMMARY ON REMNANTS 1. REMNANTS AS DARK MATTER * compatible with PBH formation at reheating * stability via minimal area/mass 2. BOUNCE2 : Bouncing BH in a Bouncing Universe - their presence in the contracting phase yields ns scale invariance - large “old” volume inside remnants make sense of the Past Hypothesis 3. FAST EXPLODING PBH - phenomenology depends on the lifetime as short as m2 - new experimental window for quantum gravity - signals in the sub-mm, radio & TeV direct detection & diffuse emission what else peculiar energy distance relation can change if black holes also late-universe observations explode this way? Quantum Gravity Phenomenology Francesca Vidotto MAIN REFERENCES Planck Stars Planck stars Carlo Rovelli, Francesca Vidotto Int. J. Mod. Phys. D23 (2014) 12, 1442026 Cosmic Rays Planck star phenomenology Planck stars as observational probes of Aurelien Barrau, Carlo Rovelli. quantum gravity Carlo Rovelli Phys. Lett. B739 (2014) 405 Nature Astronomy, March’17, comment Fast Radio Bursts and White Hole Signals Aurélien Barrau, Carlo Rovelli, Francesca Vidotto. Phys. Rev. D90 (2014) 12, 127503 Phenomenology of bouncing black holes in quantum gravity: a closer look Aurélien Barrau, Boris Bolliet, Francesca Vidotto, Celine Weimer JCAP 1602 (2016) no.02, 022 Fast radio bursts and the stochastic lifetime of black holes in quantum gravity Aurélien Barrau, Flora Moulin, Killian Martineau Phys.Rev. D97 (2018) no.6, 066019 Late Cosmo. Quantum effects of Primordial Black Holes on Galaxy Clustering Alvise Raccanelli, Licia Verde, Francesca Vidotto to appear in JCAP, e-Print: arXiv: 1708.02588 Remnants White Holes as Remnants: A Surprising Scenario for the End of a Black Hole Eugenio Bianchi, Marios Christodoulou, Fabio D’Ambrosio, Hal Haggard, Carlo Rovelli e-Print: arXiv:1802.04264 Small black/white hole stability and dark matter Carlo Rovelli, Francesca Vidotto. e-Print: arXiv:1805.03872 Erebons Pre-big-bang black-hole remnants and the past low entropy Carlo Rovelli, Francesca Vidotto. e-Print: arXiv:1805.03224 Quantum Gravity Phenomenology Francesca Vidotto