Measuring the Last Burst of Non-Singular

Home , Francesca Vidotto, Planck star

CAUSALITY IN CONFORMAL DIAGRAMS

"- BH

•

"+ WH " +• ∆ t = 0 • III "-• II Metric that describe the process vacuum solution of Einstein equations

= 0 = I

r I. Minkowski II. Schwarzschild III. Quantum Gravity

Haggard, Rovelli 1407.0989

Planck Stars Francesca Vidotto NON-SINGULAR BLACK HOLES

QUANTUM REPULSION Non-perturbative effect Effective theory: quantum repulsion

TIME DILATATION Bounce time ~ M ~ ms for M 2 9 Asymptotic time ~ M ~10 for M

LIFETIME ~ M2 to be compared with the evaporation time ~ M3 (no information paradox)

Quantum BlackGravity Holes Phenomenology Francesca Vidotto NON-SINGULAR BLACK HOLES

NON-PERTURBATIVE EFFECT Vidotto, Rovelli 1401.6562 Effective theory: quantum repulsion Quantum effects piling outside the horizon

TIME DILATATION Bounce time ~ M ~ ms for M • 2 9 t = 0 Asymptotic time ~ M ~10 for M • •

horizon

LIFETIME ~ M2 0 = r to be compared with the evaporation time ~ M3 (no information paradox) r=const

Quantum BlackGravity Holes Phenomenology Francesca Vidotto HOW LONG IS THE BOUNCE FROM OUTSIDE?

Upper limit: Vidotto, Rovelli 1401.6562 Firewall argument (Almheiri, Marolf, Polchinski, Sully):“something” unusual must happen before the Page time (~ 1/2 evaporation time)

⟹ the hole lifetime must be shorter or of the order of ~ m3

Lower limit: Haggard, Rovelli 1407.0989 For something quantum to happens, semiclassical approximation must fail. -2 Typically in quantum gravity: high curvature Curvature ~ (LP) Small effects can pile up: small probability per time unit gives a probable effect on a long time! -1 Typically in quantum tunneling: Curvature × (time) ~ (LP)

⟹ the hole lifetime must be longer or of the order of ~ m2

Quantum Gravity Phenomenology Francesca Vidotto HOW LONG IS THE BOUNCE FROM OUTSIDE?

Upper limit: Vidotto, Rovelli 1401.6562 Firewall argument (Almheiri, Marolf, Polchinski, Sully):“something” unusual must happen before the Page time (~ 1/2 evaporation time)

⟹ the hole lifetime must be shorter or of the order of ~ m3

Quantum Gravity Phenomenology Francesca Vidotto HOW LONG IS THE BOUNCE FROM OUTSIDE?

Upper limit: Vidotto, Rovelli 1401.6562 Firewall argument (Almheiri, Marolf, Polchinski, Sully):“something” unusual must happen before the Page time (~ 1/2 evaporation time)

⟹ the hole lifetime must be shorter or of the order of ~ m3

Quantum Gravity Phenomenology Francesca Vidotto 1. GEOMETRY QUANTIZED

The matrix of the components Li , a = 1, .., 3 is L = 1 (det M)M 1, where M is the matrix • a 2 formed by the components of three edges of the tetrahedron that emanate from a common vertex.

Exercise: Show all these deﬁnitions are equivalent.

The vectors~La have the following properties. They satisfy the “closure” relation • 4 ~ ~ C := Â La = 0. (1.3.5) a=1

The quantities ~L determine all other geometrical • a quantities (for a tetrahedron), such as areas, volume, angles between edges and dihedral angles between faces. The geometry of the tetrahedron, and all these quantities, are invariant under a common SO(3) rotation of the four~La. Therefore the tetrahedron is determined by an equivalence class of ~La’s satisfying (1.3.5), under rotation. Check that the resulting number of degrees of freedom is correct. ~ Figure 1.3. The four vectors La, normals to The area A of the face a is ~L . • a | a| the faces. The volume V is determined by the (properly ori- • ented) triple product of any three faces:

2 2 j j 2 V2 = (~L ~L ) ~L = e Li L Lk = eabce Li L Lk = det L. (1.3.6) 9 1 ⇥ 2 · 3 9 ijk 1 2 3 ijk a b c 9

Exercise: Prove these relations. Hint: choose a tetrahedron determined by a triple of orthonormal edges, and then argue that the result is general because the formula is invariant under linear transformations.

If the tetrahedron is small compared to the local curvature, the metric can be assumed to be ~ i i a locally flat and La can be identified with the flux of the triad field e = eadx across the face a (triads and tetrads will be discussed in detail in Chapter 3)

i 1 i i i La = e jk e e (1.3.7) 2 Za ^ Since the triad is the gravitational ﬁeld, this gives the explicit relation between these quantities and the gravitational ﬁeld.

QuantizationLOOP of the QUANTUM geometry GRAVITY We have all the ingredients for jumping to quantum gravity. The geometry of a real physical tetrahedron is determined by the gravitational ﬁeld, which is a quantum ﬁeld. Therefore the normals ~La are to be described by quantum operators, when we do not disregard quantum gravity. These will obey commutation relations. The commutation relation can be obtained from the hamilto- nian analysis of GR, by promoting Poisson brackets to operators, in the same manner in which (1.2.1) and (1.3.3) can; but ultimately they are quantization postulates, like (1.2.1) and (1.3.3). Let us therefore just postulate them here. The= L simplest[SU(2)L possibility/SU(2)N ] is to mimic (1.3.3), namely to write H 2 i j 2 ij k [La, Lb]=i dabl # k La, (1.3.8) Hilbert Space Wv =(PSL(2,C) Y v)(1I) Operator Algebra and there was SpaceTime 11

Transition Amplitude

Quantum Black Holes Francesca Vidotto A PROCESS AND ITS AMPLITUDE

Boundary state = in ⌦ out Quantum system Amplitude A = W ( ) = Spacetime region

Boundary Particle detectors = ﬁeld measurements

Distance and time measurements Spacetime region = gravitational ﬁeld measurements

In GR, distance and time measurements are ﬁeld measurements like any other one: they are part of the boundary data of the problem

Boundary values = geometry of box surface = distance and time separation of the gravitational ﬁeld of measurements

Quantum Black Holes Francesca Vidotto BOUNDARY STATE

Boundary: B3 U B3 (joined on a S2)

Each B3 can be triangulated by 4 isosceles tetrahedra

Minkowski The bulk can be approximated to ﬁrst order by two 4-simplices joined by a tetrahedron

Schwarzschild • • t = 0 •

Minkowski r = 0 = r

Quantum Black Holes Francesca Vidotto BOUNDARY STATE

Boundary: B3 U B3 (joined on a S2)

Each B3 can be triangulated by 4 isosceles tetrahedra

Minkowski The bulk can be approximated to ﬁrst order by two 4-simplices joined by a tetrahedron

Schwarzschild • • t = 0 •

Minkowski r = 0 = r

Quantum Black Holes Francesca Vidotto Amplitude W (m, T ) BLACK HOLE LIFETIME

Jn Jn,Kn Kn, ln W (m, T )= w(m, T, j ) N ( ⌫n , ↵n ) f i { } ` jn jn ln { } { } { } { }{ } ! ! j Jn , Kn , l n n {X`} { } {X} { `} O O

2 1 (2⌘` 1) 2 (j` ) w(m, T, j )=c(m) d e 2⌘` 2 ei⇣`j` , ⌘2 m2 ` j` ` ⇠ Y`

Jn j` 2 Jn, jn N = D ( ⌫n , ↵n ) i { } jn 0 m`j` { } { } 1 !mn { } `Tn ~ m { } O2 @ A

sinh2 r Kn,Jn Jn, jn n ! Kn, ln f dJ i { } drn dj l p (rn) i { } dK jn ln ⌘ n !p n 0 4⇡ ` ` ` 1 p n n { }{ } { } Z ` n { } O2 @ A

⌧ (m) 1 P (m, T ) dT =1 Z0 e

Quantum BlackGravity Holes Phenomenology Francesca Vidotto

Marios Christodoulou (CPT, AMU) Black to White Hole transition: Bounce Time a Realistic ObservableMay 23, from 2016 non-perturbative 14 / 14 QG 2 © 1974 Nature Publishing Group m ~Hubble time 3 50 Hubble times, while 24 , m ~10 For m ~10 Kg

All black holes are subject to quantum effects.

An explosion observed today, requires old black holes: primordial.

(Quantum) PBH dark matter:

Today, black holes smaller than m ( t ) t = t have already exploded. | H It decreases with time. ( but for later accretion/merging )

Caution with constraints! Constraints from Hawking evaporation do not apply. PBH should exists, but not necessarily constitute all DM.

Quantum Black Holes Francesca Vidotto QUANTUM PRIMORDIAL BLACK HOLES AS DARK MATTER

Structure formation Raccanelli, Chluba, Cholis, Vidotto WIP

First stars & Supermassive black holes Bambi, Freese, Vidotto WIP

Primordial black holes inside first-generation stars can provide the seeds for supermassive black holes.

Quantum BlackGravity Holes Phenomenology Francesca Vidotto EXPECTED SIGNALS

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 THE SMOKING GUN: DISTANCE/ENERGY RELATION

Low energy channel

distant signals originated in younger and smaller sources

Quantum BlackGravity Holes Phenomenology Francesca Vidotto maximal extension of the Schwarzschild metric for a The energy (and amplitude) of the signal emitted in mass M. Region (III) is where quantum gravity becomes the quantum gravity model considered here remains non-negligible. open. As suggested in [11] and to remain general, we consider two possible signals of di↵erent origins. Importantly, by gluing together the di↵erent part of The first one, referred to as the low energy signal, the e↵ective metric and estimating the time needed for is determined by dimensional arguments. When the maximal extension of the Schwarzschildquantum e↵ects metric to happen, for a it wasThe shown energy that the (and dura- amplitude)bounce of is the completed, signal emitted the black in hole (more precisely the mass M. Region (III) is wheretion quantum of the gravity bounce becomes should not bethe shorter quantum than [10] gravity modelemerging considered white hole) here has remains a size (L 2M)determinedby non-negligible. open. As suggested inits [11] mass andM. to This remain is the general, main scale⇠ of the problem and it ⌧ =4kM2we, consider two possible(1) fixes signals an expected of di↵erent wavelength origins. for the emitted radiation: The first one, referred to asL the. Welow assume energy thatsignal, particles are emitted at the Importantly, by gluing together the di↵erent part of ⇠ the e↵ective metric and estimatingwith k> the time0.05 needed a dimensionless for is parameter. determined We by dimensional use prorata arguments. of their number When of internal the degrees of freedom. Planck units where G = ~ =bouncec = 1. is completed, The bounce the black(This hole is also (more the case precisely for the the Hawking spectrum at the quantum e↵ects to happen, it was shown that the dura-2 3 tion of the bounce should nottime be shorter is proportional than [10] to M andemerging not to M whiteas hole) in the has aoptical size (L limit,2Mi.e.)determinedbywhen the greybody factors describ- Hawking process. As long as kitsremains mass M small. This enough, is the maining scalethe backscattering⇠ of the problem probability and it are spin-independent.) the bounce time is much smaller than the Hawking 2 fixes an expectedPRIMORDIALTHE wavelength SMOKING GUN: for BLACK the DISTANCE/ENERGY emitted radiation: RELATION ⌧ =4kMevaporation, time and the(1) evaporation can be considered The second signal, referred to as the high energy com- L. We assume that particles are emitted at the as a dissipative correction that can⇠ be neglected in a ponent, has a very di↵erent origin. Consider the history with k>0.05 a dimensionlessfirst order parameter. approximation. We use prorata of their number ofof internal the matter degrees emerging of freedom. from a white hole: it comes from Planck units where G = ~ = c = 1. The bounce (This is also the case forHigh the energy bounce Hawking channel of thespectrum matter at that the formed the black hole by 2 3 time is proportional to M andThe not phenomenology to M as in was the investigatedoptical in limit, [11] underi.e. thewhen thecollapsing. greybody In most factors scenarios describ- there is a direct relation be- Hawking process. As long asassumptionk remains that smallk takes enough, its smallesting possible the backscattering value, which probabilitytween the are formation spin-independent.) of a primordial black hole of mass M the bounce time is much smallermakes the than bounce the Hawking time as short as possible. The aim and the temperature of the Universe when it was formed evaporation time and the evaporationof the present can be article considered is to go beyondThe this second first signal, study in referred(see to [14] as for the ahigh review). energyM com-is given by the horizon mass as a dissipative correction thattwo can directions. be neglected First, we in generalize a ponent, the previous has a very results di↵erentMH origin.: Consider the history by varying k. The only conditionof the for matter the model emerging to be from a white hole: it comes from first order approximation. M M t. (2) valid is that the bounce time remainsthe bounce (much) of the smaller matter that formed the black⇠ holeH by⇠ than the Hawking time. This assumption is supported The phenomenology was investigated in [11] under the collapsing. In most scenarios(Other there more is a direct exotic relation models, be-e.g. collisions of cosmic by the “firewall argument” presented in [1]. We study in tween the formation of a primordialstrings or black collisions hole of of bubbles mass M associated with di↵erent assumption that k takes its smallestdetail possible the maximal value, distance which at which a single black-hole vacua, can lead to di↵erent masses at a given cosmic time. makes the bounce time as shortbounce as possible. can be detected. The aim Second,and we go the beyond temperature this “sin- of the Universe when it was formed We will not consider them in this study.) The cosmic of the present article is to gogle beyond event this detection” first study and consider in (see the [14] di↵use for background a review). M is given by the horizon mass time t is related to the temperature of the Universe T by two directions. First, we generalizeproduced the by previous a distribution results of bouncingMH : black holes. by varying k. The only condition for the model to be 1 2 2 M MH t. t 0.3g(2)T , (3) valid is that the bounce time remains (much) smaller ⇠ ⇠ ⇠ ⇤ than the Hawking time. This assumptionII. SINGLE is supported EVENT DETECTION (Other more exotic models,wheree.g.g collisions100 is the of number cosmic of degrees of freedom. by the “firewall argument” presented in [1]. We study in ⇤ ⇠ strings or collisions of bubblesOnce associatedk is fixed, M with is fixed di↵ (byerent⌧ tH ) and T is therefore detail the maximal distance at which a single black-hole Quantum BlackGravity Holes Phenomenology ⇠ Francesca Vidotto For detection purposes, wevacua, are interested can lead in to black di↵erentknown. masses at As a the given process cosmic is time. time-symmetric, what comes bounce can be detected. Second,holes we whose go beyond lifetime this is “sin- less than the age of the Universe. out from the white hole should be what went in the We will not consider them in this study.) The cosmic gle event detection” and considerFor the a primordial di↵use background black hole detected today, ⌧ = t black hole, re-emerging at the same energy: a blackbody time t is related to theH temperature of the Universe T by produced by a distribution of bouncingwhere tH is black the Hubble holes. time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter k (defined in the previous black1 hole plays the role of a “time machine” that sends 2 2 section) for black holes that can be observed. Int all 0.3theg primordialT , universe radiation(3) to the future: while the ⇤ cases considered, M is very small compared to a solar⇠ surrounding space has cooled to 2.3K, the high-energy II. SINGLE EVENTmass DETECTION and therefore only primordialwhere blackg holes100 possibly is the numberradiation of emerges degrees from of freedom. the white hole with its original ⇤ ⇠ formed in the early Universe areOnce interestingk is fixed, from M is this fixed (byenergy.⌧ tH ) and T is therefore For detection purposes, wepoint are of interested view. Although in black no primordialknown. blackAs the hole process has is time-symmetric,⇠ what comes holes whose lifetime is less thanbeen the detected age of the to date, Universe. various mechanismout from for the their white pro- hole shouldWhen be the what parameter wentk inis taken the larger that its smallest For a primordial black holeduction detected shortly today, after⌧ the= t BigH Bangblack have hole, been re-emerging suggested atpossible the same value, energy: that a blackbodyis fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time where tH is the Hubble time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter kfor(defined a review). in the Although previous their numberblack hole density plays might the be role ofbecomes a “time larger machine” for a thatgiven sends mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we section) for black holes that can be observed. In all the primordial universe radiation to the future: while the primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means cases considered, M is very smallof cosmological compared to physics a solar eithersurrounding directly from space density has cooledthat to the 2.3K, mass thehas to high-energy be smaller. The resulting energy mass and therefore only primordialperturbations black holes –possibly possibly enhancedradiation by phase emerges transitions– from thewill white be higher hole with for both its original the low energy and the high formed in the early Universeor are through interesting exotic from phenomena this likeenergy. collisions of cosmic energy signals, but for di↵erent reasons. In the first point of view. Although no primordialstrings or bubbles black of hole false has vacua. case, because of the smaller size of the hole, leading been detected to date, various mechanism for their pro- When the parameter k isto taken a smaller larger emitted that its wavelength. smallest In the second case, duction shortly after the Big Bang have been suggested possible value, that is fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time 2 for a review). Although their number density might be becomes larger for a given mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means of cosmological physics either directly from density that the mass has to be smaller. The resulting energy perturbations –possibly enhanced by phase transitions– will be higher for both the low energy and the high or through exotic phenomena like collisions of cosmic energy signals, but for di↵erent reasons. In the first strings or bubbles of false vacua. case, because of the smaller size of the hole, leading to a smaller emitted wavelength. In the second case,

2 maximal extension of the Schwarzschild metric for a The energy (and amplitude) of the signal emitted in mass M. Region (III) is where quantum gravity becomes the quantum gravity model considered here remains non-negligible. open. As suggested in [11] and to remain general, we consider two possible signals of di↵erent origins. Importantly, by gluing together the di↵erent part of The first one, referred to as the low energy signal, the e↵ective metric and estimating the time needed for is determined by dimensional arguments. When the maximal extension of the Schwarzschildquantum e↵ects metric to happen, for a it wasThe shown energy that the (and dura- amplitude)bounce of is the completed, signal emitted the black in hole (more precisely the mass M. Region (III) is wheretion quantum of the gravity bounce becomes should not bethe shorter quantum than [10] gravity modelemerging considered white hole) here has remains a size (L 2M)determinedby non-negligible. open. As suggested inits [11] mass andM. to This remain is the general, main scale⇠ of the problem and it ⌧ =4kM2we, consider two possible(1) fixes signals an expected of di↵erent wavelength origins. for the emitted radiation: The first one, referred to asL the. Welow assume energy thatsignal, particles are emitted at the Importantly, by gluing together the di↵erent part of ⇠ the e↵ective metric and estimatingwith k> the time0.05 needed a dimensionless for is parameter. determined We by dimensional use prorata arguments. of their number When of internal the degrees of freedom. Planck units where G = ~ =bouncec = 1. is completed, The bounce the black(This hole is also (more the case precisely for the the Hawking spectrum at the quantum e↵ects to happen, it was shown that the dura-2 3 tion of the bounce should nottime be shorter is proportional than [10] to M andemerging not to M whiteas hole) in the has aoptical size (L limit,2Mi.e.)determinedbywhen the greybody factors describ- Hawking process. As long as kitsremains mass M small. This enough, is the maining scalethe backscattering⇠ of the problem probability and it are spin-independent.) the bounce time is much smaller than the Hawking 2 fixes an expectedPRIMORDIALTHE wavelength SMOKING GUN: for BLACK the DISTANCE/ENERGY emitted radiation: RELATION ⌧ =4kMevaporation, time and the(1) evaporation can be considered The second signal, referred to as the high energy com- L. We assume that particles are emitted at the as a dissipative correction that can⇠ be neglected in a ponent, has a very di↵erent origin. Consider the history with k>0.05 a dimensionlessfirst order parameter. approximation. We use prorata of their number ofof internal the matter degrees emerging of freedom. from a white hole: it comes from Planck units where G = ~ = c = 1. The bounce (This is also the case forHigh the energy bounce Hawking channel of thespectrum matter at that the formed the black hole by 2 3 time is proportional to M andThe not phenomenology to M as in was the investigatedoptical in limit, [11] underi.e. thewhen thecollapsing. greybody In most factors scenarios describ- there is a direct relation be- Hawking process. As long asassumptionk remains that smallk takes enough, its smallesting possible the backscattering value, which probabilitytween the are formation spin-independent.) of a primordial black hole of mass M the bounce time is much smallermakes the than bounce the Hawking time as short as possible. The aim and the temperature of the Universe when it was formed evaporation time and the evaporationof the present can be article considered is to go beyondThe this second first signal, study in referred(see to [14] as for the ahigh review). energyM com-is given by the horizon mass as a dissipative correction thattwo can directions. be neglected First, we in generalize a ponent, the previous has a very results di↵erentMH origin.: Consider the history by varying k. The only conditionof the for matter the model emerging to be from a white hole: it comes from first order approximation. M M t. (2) valid is that the bounce time remainsthe bounce (much) of the smaller matter that formed the black⇠ holeH by⇠ than the Hawking time. This assumption is supported The phenomenology was investigated in [11] under the collapsing. In most scenarios(Other there more is a direct exotic relation models, be-e.g. collisions of cosmic by the “firewall argument” presented in [1]. We study in tween the formation of a primordialstrings or black collisions hole of of bubbles mass M associated with di↵erent assumption that k takes its smallestdetail possible the maximal value, distance which at which a single black-hole vacua, can lead to di↵erent masses at a given cosmic time. makes the bounce time as shortbounce as possible. can be detected. The aim Second,and we go the beyond temperature this “sin- of the Universe when it was formed We will not consider them in this study.) The cosmic of the present article is to gogle beyond event this detection” first study and consider in (see the [14] di↵use for background a review). M is given by the horizon mass time t is related to the temperature of the Universe T by two directions. First, we generalizeproduced the by previous a distribution results of bouncingMH : black holes. by varying k. The only condition for the model to be 1 2 2 M MH t. t 0.3g(2)T , (3) valid is that the bounce time remains (much) smaller ⇠ ⇠ ⇠ ⇤ than the Hawking time. This assumptionII. SINGLE is supported EVENT DETECTION (Other more exotic models,wheree.g.g collisions100 is the of number cosmic of degrees of freedom. by the “firewall argument” presented in [1]. We study in ⇤ ⇠ strings or collisions of bubblesOnce associatedk is fixed, M with is fixed di↵ (byerent⌧ tH ) and T is therefore detail the maximal distance at which a single black-hole Quantum BlackGravity Holes Phenomenology ⇠ Francesca Vidotto For detection purposes, wevacua, are interested can lead in to black di↵erentknown. masses at As a the given process cosmic is time. time-symmetric, what comes bounce can be detected. Second,holes we whose go beyond lifetime this is “sin- less than the age of the Universe. out from the white hole should be what went in the We will not consider them in this study.) The cosmic gle event detection” and considerFor the a primordial di↵use background black hole detected today, ⌧ = t black hole, re-emerging at the same energy: a blackbody time t is related to theH temperature of the Universe T by produced by a distribution of bouncingwhere tH is black the Hubble holes. time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter k (defined in the previous black1 hole plays the role of a “time machine” that sends 2 2 section) for black holes that can be observed. Int all 0.3theg primordialT , universe radiation(3) to the future: while the ⇤ cases considered, M is very small compared to a solar⇠ surrounding space has cooled to 2.3K, the high-energy II. SINGLE EVENTmass DETECTION and therefore only primordialwhere blackg holes100 possibly is the numberradiation of emerges degrees from of freedom. the white hole with its original ⇤ ⇠ formed in the early Universe areOnce interestingk is fixed, from M is this fixed (byenergy.⌧ tH ) and T is therefore For detection purposes, wepoint are of interested view. Although in black no primordialknown. blackAs the hole process has is time-symmetric,⇠ what comes holes whose lifetime is less thanbeen the detected age of the to date, Universe. various mechanismout from for the their white pro- hole shouldWhen be the what parameter wentk inis taken the larger that its smallest For a primordial black holeduction detected shortly today, after⌧ the= t BigH Bangblack have hole, been re-emerging suggested atpossible the same value, energy: that a blackbodyis fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time where tH is the Hubble time. This fixes the mass M, as spectrum at temperature T . Intuitively, the bouncing a function of the parameter kfor(defined a review). in the Although previous their numberblack hole density plays might the be role ofbecomes a “time larger machine” for a thatgiven sends mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we section) for black holes that can be observed. In all the primordial universe radiation to the future: while the primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means cases considered, M is very smallof cosmological compared to physics a solar eithersurrounding directly from space density has cooledthat to the 2.3K, mass thehas to high-energy be smaller. The resulting energy mass and therefore only primordialperturbations black holes –possibly possibly enhancedradiation by phase emerges transitions– from thewill white be higher hole with for both its original the low energy and the high formed in the early Universeor are through interesting exotic from phenomena this likeenergy. collisions of cosmic energy signals, but for di↵erent reasons. In the first point of view. Although no primordialstrings or bubbles black of hole false has vacua. case, because of the smaller size of the hole, leading been detected to date, various mechanism for their pro- When the parameter k isto taken a smaller larger emitted that its wavelength. smallest In the second case, duction shortly after the Big Bang have been suggested possible value, that is fixed for quantum e↵ects to be (see, e.g., [12] for an early detailed calculation and [13] important enough to lead to a bounce, the bounce time 2 for a review). Although their number density might be becomes larger for a given mass. If this time is assumed way too small for direct detection, the production of to be equal to the Hubble time (or slightly less if we primordial black holes remains a quite generic prediction focus on black holes bouncing far away), this means of cosmological physics either directly from density that the mass has to be smaller. The resulting energy perturbations –possibly enhanced by phase transitions– will be higher for both the low energy and the high or through exotic phenomena like collisions of cosmic energy signals, but for di↵erent reasons. In the first strings or bubbles of false vacua. case, because of the smaller size of the hole, leading to a smaller emitted wavelength. In the second case,

2 THE SMOKING GUN: DISTANCE/ENERGY RELATION 4 by 1 1/2 other other 2Gm H0 1 ⌦⇤ (1 + z) sinh (z + 1) 3/2 obs =(1+z)emitted. ⟶ obs(6) 2 1/2 ⇠ c v ⌦M u6 k⌦⇤ " # u ✓ ◆ The speciﬁc redshift dependence of our model makes t 2 it possibly testable against other proposals. Obvi- 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 account 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 negligibleredshift when the compared resulting to function the expected dark matter density, even when integrated 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 Barrau, Rovelli, Vidotto 1409.4031 z it requires astrophysical considerations beyond this first DISCRIMINATION WITH DARK MATTER AND 2 2 4 6 8 10 d N ↵ 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) events were measured, it would be important to ensure distance:8kM the youth of the hole compensate for the redshift. reason for that is the redshift dependance. When looking 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. M0+dM energy is E. But this is not true for the bouncing black ↵ Nexp = pM dM. (9) holes signal. The reason for this is that black holes that M The received signal is going to be corrected by standard Let us turn to something that has been observed. 0 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- from the Arecibo Observatory have confirmed the detec- 2Gm phenomenon could explain the GeV excess measured by 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) , namely a wavelength v ⌦M 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 remainsproper much below time. the observed A straightforward calculation gives the speed of light c; H0, ⌦⇤ and ⌦M being the Hubble background. Unquestionably, there are other – less exotic observed 20 cm. (7) constant, the cosmological constant, and the matter den- – ways to explain the Fermi excess. But the important 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 sucient 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 sucient –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 dicult. 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 DETECTION ON

Quantum BlackGravity Holes Phenomenology Francesca Vidotto 1 1 4 1 1 2 1 4 meas 2⇡ (1 + z) H0 1 ⌦⇤ 1 3 2 meas 2⇡ (1sinh +z) H0 (1 +1z) 2⌦⇤ . 3 (6) high 1 1 1/2 sinh (1 + z) 2 . (6) ⇠ k T high2 1 1 ⌦ 1/2 B (0.3g ) "6k⌦ 2" M ## ⇤ ⇠ kBT⇤ (0.3g ) ✓"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) dn M(t+t) dn n(R)= n(R)= dM, (8)dM, (8) The following conclusionsThe following can be conclusions drawn: can be drawn: dMdV 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 theR mass cor- • low- and high energy channels decreases for higher responding toR a time (tH c ). If one assumes that pri- low- and high energy channels decreases for higher responding to a time (tH ). If one assumes that pri- values of k, i.e. for longer black-hole lifetimes. mordial black c holes 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 a the high-enough collapse density con- INTEGRATEDIn the low energy EMISSIONchannel, for the smallerof density values fluctuations with a high-enough density con- Barrau, Bolliet,trast Vidotto, Weimer in the 1507 early.1198 Universe, the initial mass spectrum is In the low energy• channel,of k, a single for the bounce smaller can be values detectedtrast arbitrary in the far early Universe, the initial mass spectrum is • of k, a single bounce can be detected arbitrary⌧ m far2 directly related to the equation of state of the Universe away in the Universe. ⇠ directly related toat the the equationformation of epoch. state It of is the given Universe by [18, 19]: away in the Universe. at the formation epoch. It is given by [18, 19]: Low energyIn all cases,channel the distances are large enoughHigh energy and ex-channel

• k=0.05 1+3w In all cases, the distances are large enough and ex- direct decayed dn 1 perimental detection is far from being hopeless. = ↵M 1+w , (10) • dn 1 1+3w perimental detection is far from being hopeless. = ↵M dMdV 1+w , (10) k=0.05 k=100 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. exponent The1 normalization1+3w takes⌘ the coe valuecient↵=will5 be/2. kept unknown In addition to the instantaneous spectrum emitteddirect+decayed by a 1+w enlarged The normalization⌘as it coe dependscient on↵ thewill details be kept of the unknown black hole formation In addition to thesingle instantaneous bouncing spectrum black hole, emitted it is interesting by a to consider the as it depends onmechanism. the details of For the a sizeableblack hole amount formation of primordial black single bouncing blackpossible hole, it di is↵ interestinguse background to consider due to the the integrated emis- k=10000 mechanism.k=109 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 unitdN surface,mes can be written as: mass spectrum takes a high enough value in the relevant = ind((1+z)E,R) n(R) Acc Absscale(E,R invariance)dR, (BSI) scenario. The idea is that the dN dEdtdS · · · masscharacteristic spectrum shape: takesrange distorted a whereas high black enough itbody 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 fluxdepends emitted on how muchWe will DM notare PBL study 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 where ind(E,R) denotes the individual flux emitted We will not study those questions here and just consider energyQuantumE BlackGravity, Acc Holes Phenomenologyis the angular acceptance of the detector whichFrancesca depends Vidotto sensitively on the bounds of the mass by a single bouncingmultiplied black hole by its at e distanceciencyR (inand principle at thisthe shape is also of a the resultingspectrum, emission, that are 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 eisciency 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 ignoredbouncing 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 usethe exact distance 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 distributedone 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 meas 2⇡ (1 + z) H0 1 ⌦⇤ 3 n(R)= dM, (8) The following conclusions can be drawn: 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 dMdV 8k high 1 1 1/2 sinh compensated(1 by + z the) larger. amount of photons. (6) dn ⇡ decreases⇠ kBT (0 as.3g a function) 2 of k in both⌦ cases,M it does not detail. If one denotes by dMdV the initial di↵erential "6k⌦⇤ "✓ ◆ 1## 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 This shows that although the mean wavelength does It is worth considering the n(R) term a bit more inM(t+t) dn n(R)= of densitydM, fluctuations with(8) a high-enough density con- decreases as a function of k in bothThe following cases, it does conclusions not candetail. beIn drawn: the If onelowPBH denotes energy MASSchannel, by SPECTRUMdn forthe the initial smaller di↵erential values trastdMdV in the early Universe, the initial mass spectrum is 1 • of k, a singlePBH bounce MASS candMdV SPECTRUM be detected arbitraryZ farM(t) follow the same general behavior. It scales with k 2 mass spectrum of primordial black holes per unit volume, directly related to the equation of state of the Universe The low1 energy channel leadsaway to in a the better Universe. single- for the low energy component and• aseventk 4 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 maximal distances between the where the mass spectrum is evaluated for the mass cor- • event detection than the high energy channel. leading toIII. INTEGRATED EMISSION where w = p/⇢. In a matter-dominated universe the • low- and high energy channels decreasesLow for energy higher channelresponding to a time (t R ). If one assumes that1+3 pri-w Although lower energy dilutes the signal in a H exponentc 1 1+w takes the value = 5/2. values of k, i.e. for longer black-hole lifetimes. mordial black holes are directly formed by⌘ the collapse higher astrophysical background, this e↵ect is over- dn t The normalization coecient ↵ will be kept unknown In addition to the instantaneousn(R) of spectrum density, fluctuations emitted by(9) a with a high-enough density con- compensated by the larger amount of photons.1 ⇡ dMdV 8k as it depends on the details of the black hole formation 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 backgroundarbitrary 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 (tH ).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 photons 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 isof farchannel. 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 thedNtrastmes 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 = ((1+z)E,R) n(R) Acc Abs(E,R)dR, higher astrophysical background, thisdEdtdSdirectly e↵ect is related over-ind to the equation of state of the Universe range whereas it is naturally suppressed at small masses away in the Universe. · where· w ·= p/⇢. In a matter-dominated universe the compensated byIII. the larger INTEGRATED amountat of thephotons. EMISSION formationZ epoch. It is given by [18, 19]: (7) by inflation and at large 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 betweenind(E,R the ) denotes the individual flux⌘ emitted 1+w We will not study those questions here and just consider • dn The1+3 normalizationw coecient ↵ will be kept unknown perimental detection• is far fromIn addition being hopeless. to the instantaneousby a single spectrum bouncing emitted black by a hole1 at1+ distancew R and at the shape of the resulting emission, nor its normalisation low- and high energy channels decreases for higher = ↵M as it depends, on the(10) details of the black hole formation valuessingle of k bouncing, i.e. for longer black black-holehole, itenergy is interesting lifetimes.E, Acc tois consider thedMdV angular the acceptance of the detector which depends sensitively on the bounds of the mass mechanism. For a sizeable amount of primordial black possible di↵use backgroundmultiplied due to the by integrated its eciency emis- (in principle this is also a spectrum, that are highly model-dependent. As this part where w = p/⇢. In a matter-dominatedholes to form, universe the power the spectrum normalized on the III. INTEGRATEDIn thesion EMISSIONlow of energy a populationchannel, of for bouncing thefunction smaller black of valuesE holes.but this Formally, will be ignored here), Abs(E,R) of the study is devoted to the investigation of the shape • of k, a single bounce can be detectedexponent arbitrary far 1 1+3w takesCMB the needs value to = be boosted5/2. at small scales. This can the number of measured photonsis the detected absorption per function, unit time,1+w and n(R) is the number of of the signal, the y axis on the figures are not normalized. away in the Universe. The normalization⌘ coecient ↵bewill achieved, be kept for unknown example, through Staobinsky’s broken In addition to the instantaneousunit spectrum energy and emitted unit by surface, a black can holes be written bouncingQuantum as:FIG. atGravity 5: distance LowPhenomenology energyR perchannel unit signal time calculated and for di↵erent 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, it is interesting to consider the volume. The distance R and the redshift z entering Fortunately, the results are weakly dependent upon In alldN cases, the distances are largemechanism. enough and ex- For aunits sizeable of the amounty axismass are spectrum of arbitrary. primordial takes black a high enough value in the relevant possible di↵use background• perimental due tomes the detection integrated is far emis- from beingthe above hopeless. formula are linked. The integration has to the shape of the mass spectrum. This is illustrated in = ind((1+z)E,Rholes) n(R to) Acc form,Abs the(E,R power)dR, 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. INTEGRATEDind(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 dNmes In additionenergy to theE, instantaneousAcc is the angular spectrummass acceptance emitted spectrum by of a the takesmation detector a high mechanism enoughwhich value (see depends [39] in the for sensitively relevant a review on on PBHs the bounds and of the mass = ind((1+z)E,R) n(R) Acc Abs(E,R)dR, which, subsequently, fixes the emitted energy. holes are assumed to be uniformly distributed in the dEdtdS single bouncingmultiplied· black· · hole,by its it is e interestingciency (inrange to considerprinciple whereas the this it is isinflation). naturally also a As suppressedspectrum, an example, at that we small are shall masses highly assume model-dependent. that primor- As this part Z Universe, which is a meaningful hypothesis as long as 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 detected at 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 eciency (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 carriedind 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 aand singleas 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 the above formula are linked.which, The integration subsequently, has fixes to thethe emitted shape energy. of the massexponent spectrum. holes1 This are1+3 is assumedw illustratedtakes the to value bein 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 eciency, 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 to usefunction, 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 as the distance fixes theR and bounce the time redshift of thez entering black hole the abovecase formula ( = are5/2, correspondingholes to form,5 to thew power=1/3). spectrum The black normalized on the which, subsequently, fixeslinked. the emitted The integration energy. has to be carriedholes out are up assumed to CMB to be needs uniformly to be boosted distributed at small in scales. the The formula cosmological distances and it is thereforeUniverse, necessary which to isgiven a meaningful above might hypothesis therefore as be long correct as only within a 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 Thornton et al. 1307.1628 FAST RADIO BURSTS Spitler et al. 1404.2934 E. Petroff et al. 1412.0342

Short Observed width ≃ milliseconds No Long GRB associated No Afterglow Punctual No repetition

Enormous flux density A real-time FRB 5 Energy ≲ 1038 erg

Likely Extragalactic Dispersion Measure: z≲0.5

104 event/day A pretty common object?

Circular polarization

Intrinsic Figure 2. The full-Stokes parameters of FRB 140514 recorded in the centre beam of the multibeam receiver with BPSR. Total intensity, and Stokes Q, U,andV are represented in black, red, green, and blue, respectively. FRB 140514 has 21 7% (3-)circularpolarisation Quantum Black Holes Francesca± Vidotto averaged over the pulse, and a 1- upper limit on linear polarisation of L<10%. On the leading edge of the pulse the circular polarisation is 42 9% (5-)ofthetotalintensity.Thedatahavebeensmoothedfromaninitialsamplingof64µsusingaGaussianﬁlteroffull-width ± half-maximum 90 µs.

source given the temporal proximity of the GMRT observa- 4.5 Gamma-Ray Burst Optical/Near-Infrared tion and the FRB detection. The other two sources, GMRT2 Detector and GMRT3, correlated well with positions for known ra- After 13 hours, a trigger was sent to the Gamma-Ray Burst dio sources in the NVSS catalog with consistent flux densi- Optical/Near-Infrared Detector (GROND) operating on the ties. Subsequent observations were taken through the GMRT 2.2-m MPI/ESO telescope on La Silla in Chile (Greiner et al. ToO queue on 20 May, 3 June, and 8 June in the 325 MHz, 2008). GROND is able to observe simultaneously in J, H, 1390 MHz, and 610 MHz bands, respectively. The second and K near-infrared (NIR) bands with a 100 100 field of epoch was largely unusable due to technical diculties. The ⇥ view (FOV) and the optical g0, r0, i0,andz0 bands with a search for variablility focused on monitoring each source for 60 60 FOV. A 2 2 tiling observation was done, providing flux variations across observing epochs. All sources from the ⇥ ⇥ 61% (JHK)and22%(g0r0i0z0) coverage of the inner part first epoch appeared in the third and fourth epochs with no of the FRB error circle. The first epoch began 16 hours af- measureable change in flux densities. ter FRB 140514 with 460 second exposures, and a second epoch was taken 2.5 days after the FRB with an identical 4.4 Swift X-Ray Telescope observing setup and 690 s (g0r0i0z0)and720s(JHK)exposures, respectively. Limiting magnitudes for J, H,andK The first observation of the FRB 140514 field was taken us- bands were 21.1, 20.4, and 18.4 in the first epoch and 21.1, ing Swift XRT (Gehrels et al. 2004) only 8.5 hours after the 20.5, and 18.6 in the second epoch, respectively (all in the FRB was discovered at Parkes. This was the fastest Swift AB system). Of all the objects in the field, analysis iden- follow-up ever undertaken for an FRB. 4 ks of XRT data tified three variable objects, all very close to the limiting were taken in the first epoch, and a further 2 ks of data magnitude and varying on scales of 0.2 - 0.8 mag in the NIR were taken in a second epoch later that day, 23 hours af- bands identified with di↵erence imaging. Of the three ob- ter FRB 140514, to search for short term variability. A final jects one is a galaxy, another is likely to be an AGN, and epoch, 18 days later, was taken to search for long term vari- the last is a main sequence star. Both XRT1 and GMRT1 ability. Two X-ray sources were identified in the first epoch sources were also detected in the GROND infrared imaging of data within the 150 diameter of the Parkes beam. Both but were not observed to vary in the infrared bands on the sources were consistent with sources in the USNO catalog timescales probed. (Monet et al. 2003). The first source (XRT1) is located at RA = 22:34:41.49, Dec = -12:21:39.8 with RUSNO =17.5 and the second (XRT2) is located at RA = 22:34:02.33 Dec =-12:08:48.2withR =19.7.BothXRT1andXRT2 USNO 4.6 Swope Telescope appeared in all subsequent epochs with no observable variability on the level of 10% and 20% for XRT1 and XRT2, An optical image of the FRB field was taken 16h51m after respectively, both calculated from photon counts from the the burst event with the 1-m Swope Telescope at Las Cam- XRT. Both sources were later found to be active galactic panas. The field was re-imaged with the Swope Telescope on nuclei (AGN). 17 May, 2 days after the FRB. No variable optical sources

c 0000 RAS, MNRAS 000,000–000 FAST RADIO BURSTS Barrau, Rovelli, Vidotto 1409.4031

#≈20 cm size of the source ≈ predicted & .02 cm Short Observed width ≃ milliseconds fast process No Long GRB associated No Afterglow Very short GRB ? gravitational waves ? Punctual No repetition the source disappears with the burst

Enormous flux density Energy ≲ 1038 erg very compact object ⟶ 1047 erg

Likely Extragalactic Dispersion Measure: z≲0.5 peculiar distance/energy relation

104 event/day A pretty common object? Are they bouncing Black Holes? Circular polarization Intrinsic Quantum Black Holes Francesca Vidotto LIST OF FAST RADIO BURSTS

name date RA dec DM width peak notes −3 FRB 010724 2001/07/24UTC for J200001h18′ -75°12J2000′ cm375pc ms4.6 ﬂux30 "Lorimer Burst" 19:50:01.63 FRB 010621 2001/06/21 18h52′ -08°29′ 746 7.8 0.4 13:02:10.79 FRB 110220 2011/02/20 22h34′ -12°24′ 944.38 5.6 1.3 01:55:48.95 FRB 110627 2011/06/27 21h03′ -44°44′ 723.0 <1.4 0.4 21:33:17.47 FRB 110703 2011/07/03 23h30′ -02°52′ 1103.6 <4.3 0.5 18:59:40.59 FRB 120127 2012/01/27 23h15′ -18°25′ 553.3 <1.1 0.5 08:11:21.72 FRB 011025 2001/10/25 19h07′ -40°37′ 790 9.4 0.3 00:29:13.23 FRB 121002 2012/10/02 18h14′ -85°11′ 1628.76 2.1; 3.7 0.35 double pulse 5.1 ms apart 13:09:18.40 FRB 121002 2012/10/02 18h14' -85°11' 1629.18 <0.3 >2.3 13:09:18.50 FRB 121102 2012/11/02 05h32′ 33°05' 557 3.0 0.4 by Arecibo radio telescope 06:35:53.24 10 repeat bursts: 6 bursts in 10 minutes, 2015 05h32′~ 33°05'~ 557~ 3 bursts weeks apart. FRB 131104 2013/11/04 06h44′ -51°17′ 779.0 <0.64 1.12 'near' Carina Dwarf Spheroidal Galaxy FRB 140514 2014/05/1418:04:01.2 22h34′ -12°18′ 562.7 2.8 0.47 21 ± 7 per cent (3σ) circular polarization FRB 090625 2009/06/25 03h07' -29°55′ 899.6 <1.9 >2.2 FRB 130626 2013/06/2621:53:52.85 16h27' -07°27' 952.4 <0.12 >1.5 FRB 130628 2013/06/2814:56:00.06 09h03' +03°26' 469.88 <0.05 >1.2 03:58:00.02 FRB 130729 2013/07/29 13h41' -05°59' 861 <4 >3.5 09:01:52.64 700-900 MHz at Green Bank radio FRB 110523 2011/05/23 21h45' -00°12' 623.30 1.73 0.6 telescope, detection of both circular and linear polarization. Detection of linear polarization. The FRB 150418 2015/04/18 07h16' −19° 00′ 776.2 0.8 2.4 origin of the burst is disputed.

Quantum BlackGravity Holes Phenomenology Francesca Vidotto TRANSIENTS AT SKA

Quantum Black Holes Francesca Vidotto NEWS IN FOCUS

ASTROPHYSICS Astronomers grapple with new eraRADIO, of fast MILLIMITERS radio AND bursts SUB-MILLIMETER ASTRONOMY Signals have progressed from astronomical peculiarity to mainstream research area.

signals, lasting no more than a few thousandths of a second. They seem to come from sources across the sky and beyond our Galaxy. Some last longer than others, and the light from a few is polarized. A discovery last year caused further excitement. Astronomers reported2 that they had found a repeating FRB — a surprise,

ANDRE RENARD/DUNLAP INSTITUTE RENARD/DUNLAP ANDRE because all the other signals had been one-off blips. And in January this year, its origin was identified3: a faint, distant dwarf galaxy around 780 megaparsecs (2.5 billion light years) away, in a star-forming region that also hums with a steady radio source. The repeater has gone some way to focusing the FRB field, says Edo Berger, an astronomer CHIME at Harvard UniversitySKA in Cambridge, Mas- sachusetts. Astronomers have now observed nearly 200 signals from it; details of 20 have been published. It bolsters the hypothesis that The CHIME radio observatory in Canada will start looking for fast radio bursts this year. the signals are extragalactic, something most FRB researchers now agree on, and its location BY ELIZABETH GIBNEY origins and precise distances. The trajectory is reshaping theories about possible causes. mirrors that of astronomers 20 years ago when Dwarf galaxies host fewer stars than most, ne of the most perplexing phenom- they were getting to grips with γ-ray bursts, so tracking an FRB to one is surprising, says ena in astronomy has come of age. which are now a staple of astronomical observa- Berger. He thinks that the unusual environment The fleeting blasts of energetic cosmic tion, says Bing Zhang, a theoretical astrophysi- is more than coincidence, and that FRBs may Oradiation of unknown cause, now known as fast cist at the University of Nevada, Las Vegas. come from super-powerful magnetars — dense, radio bursts (FRBs), were first detected a decade “The meeting has really focused the field a magnetic stars thought to form after an abnor- ago. At the time, many astronomers dismissed lot,” says Sarah Burke Spolaor, an astronomer mally massive explosion, such as an extremely the seemingly random blasts as little more than at West10 Virginia-20m University in Morgantown. energetic supernova. Studies suggest that such glitches. And although key facts, such as what Debates continue over how to root out detec- events seem to be more common in dim dwarf causes them, are still largely a mystery, FRBs tion bias and coordinate observations and on galaxies, he says. Others think the bursts might are now accepted as a genuine class of celestial what can be learnt by studying patterns in the come from active galactic nuclei, regions at signal and have spawned a field of their own. existing FRB population. the centres of some galaxies that are thought The passage was marked this month by the The first FRB was co-discovered1 in 2007 by to host supermassive black holes. Streams of first major meeting on FRBs, held in Aspen, astronomer Duncan Lorimer at West Virginia plasma from these could comb nearby pulsars Colorado, on 12–17 February. As well as cel- University.ALMA He found in archived pulsar data to produce FRBs, says Zhang, which could also ebrating a fleet of searches for the signals, the a 5-millisecond radio frequency burst that was explain a recent, although tentative, observation meeting’s 80 delegates grappled with how best so bright it couldn’t be ignored. Astronomers of a faint γ-ray burst coinciding with an FRB. to design those hunts and pin down the signals’ have since seen 25 FRBs. All are brief radio At the meeting, some astronomers proposed