Yvonne Y. Y. Wong The University of New South Wales, Sydney, Australia
Invisibles’19 School, LSC Canfranc, June 3 – 7, 2019
Or, how neutrinos fit into this grand scheme?
The grand lecture plan...
Lecture 1: Neutrinos in homogeneous cosmology
1. The homogeneous and isotropic universe 2. The hot universe and the relic neutrino background
3. Measuring the relic neutrino background via Neff
Lecture 2: Neutrinos in inhomogeneous cosmology
Lecture 1: Neutrinos in homogeneous cosmology
1. The homogeneous and isotropic universe
2. The hot universe and the relic neutrino background
3. Measuring the relic neutrino background
via Neff
Useful references...
● Lecture notes
– A. D. Dolgov, Neutrinos in cosmology, Phys. Rept. 370 (2002) 333 [hep-ph/0202122]
– J. Lesgourgues & S. Pastor, Massive neutrinos and cosmology, Phys. Rep. 429 (2006) 307 [astro-ph/0603494]. –
● Textbooks
– J. Lesgourgues, G. Mangano, G. Miele & S. Pastor, Neutrino cosmology
1. The homogeneous and isotropic universe...
The concordance flat ΛCDM model...
● The simplest model consistent with present observations.
Cosmological (Nearly) constant Massless Neutrinos (3 families) 5% 69%
26%
Composition today 13.4 billion years ago (at photon decoupling) Plus flat spatial geometry+initial conditions from single-field inflation Friedmann-Lemaître-Robertson-Walker universe...
● Cosmological principle: our universe is spatially homogeneous and isotropic on sufficiently large length scales (i.e., we are not special).
– Homogeneous → same everywhere – Isotropic → same in all directions Size of visible universe – Sufficiently large scales → > O(100 Mpc) ~ O(10 Gpc)
Isotropic but Homogeneous but Homogeneous
not homogeneous not isotropic and isotropic Friedmann-Lemaître-Robertson-Walker universe...
● Homogeneity and isotropy imply maximally symmetric 3-spaces (3 translational and 3 rotational symmetries).
– A spacetime geometry that satisfies these requirements:
2 2 2 2 dr 2 2 2 2 ds =−dt +a (t) +r (d θ +sin θ d ϕ ) FLRW metric [ 1−K r 2 ]
Spatial geometry a(t) = Scale factor K = -1 (hyperbolic), 0 (flat), +1 (spherical)
a(t 2) = Factor by which a physical length scale increases between time t1 and t2. a(t 1) ● An observer at rest with the FLRW spatial coordinates is a comoving observer. 2 2 2 2 dr 2 2 2 2 ds =−dt +a (t) +r (d θ +sin θ d ϕ ) [ 1−K r 2 ] Comoving observers
scale factor a
→ The physical distance between two comoving observers increases with time, but the coordinate distance between them remains unchanged. Cosmological redshift...
● All test particles (massive or massless) moving on geodesics of an FLRW universe suffer cosmological redshift:
Momentum of a point −1 Physical momentum of a particle measured by |⃗p|∝a particle decreases with comoving observers expanding space.
scale factor a ● Alternatively, in terms of wavelength: λ∝1/|⃗p|
Wavelength measured t0= today by comoving observer z = Redshift λ a(t ) parameter 0 = 0 ≡1+z λe a(te) Wavelength of particle (usually photon) emitted by comoving emitter
● In an FLRW universe, there is a one-to-one correspondence between t, a, and z:
redshift z time t scale factor a
→ We use them interchangeably as a measure of time. μ ν Matter/energy content: conservation law... ∇ μ T (α)=0
● Local conservation of energy-momentum in an FLRW universe implies: Energy Pressure density d ρ a˙ α +3 (ρ +P )=0 Continuity equation d t a α α – There is one such equation for each substance α.
● We need in addition to specify a relation between ρ(t) and P(t) (a property of the substance). P (t ) α w = Equation of state parameter wα (t)≡ ρα (t )
● Assuming a constant wα: How energy density −3(1+wα) ρα (t)∝a evolves with the scale factor. −3(1+wα) Matter/energy content: what is out there? ρα (t)∝a
● Nonrelativistic matter – Atoms (or constituents thereof); “baryons” in cosmology-speak. wm≃0 – Dark matter (does not emit light but −3 ⇒ρ ∝a Volume expansion feels gravity); GR people call it “dust”. m
● Ultra-relativistic radiation (at least for a significant part of their evolution history) wr=1/3 – Photons (mainly the CMB) −4 Volume expansion – ⇒ρ ∝a Relic neutrinos (analogous to CMB) r + momentum redshift – Gravitational waves??
● Other funny things wΛ=−1 – More space, Cosmological constant/vacuum energy more energy – ?? ⇒ρΛ ∝constant log(ρ) Radiation domination Matter domination Λ domination
−4 ρr ∝a ρ ∝a−3 Matter-radiation m equality Matter-Λ equality
ρΛ=const
log(a) redshift z time t log(ρ) Radiation domination Matter domination Λ domination
Big bang nucleosynthesis Last scattering surface (CMB)
−4 ρr ∝a Structure −3 Matter-radiation ρm ∝a formation equality Matter-Λ equality Today ρΛ=const
-9 -6 -3 0 log(a) redshift z a =1 By convention time t 0 Friedmann equation...
Newton's constant ● Derived from the Einstein equation: R = Ricci scalar and tensor 1 (nonlinear functions of the Rμ ν− g μ ν R=8 π G T μ ν 2nd derivative of the 2 Stress-energy tensor spacetime metric)
● The Friedmann equation is an evolution equation for the scale factor a(t):
2 2 a˙ 8 πG Friedmann H (t )≡ = ∑ ρα−K equation ( a ) 3 α H(t) = Hubble parameter
● Friedmann+continuity equations → specify the whole system.
Friedmann equation...
● You may also have seen the Friedmann equation in this form:
2 2 −3 −4 −2 H (t )=H (t0 )[ Ωm a +Ωr a +ΩΛ +ΩK a ]
2 ¯ρα (t0 ) 3 H (t ) K Ωα= , ρcrit (t )≡ , Ω K ≡− 2 2 ρcrit (t 0 ) 8 πG a H (t0 )
Critical density ● A flat universe means: From measuring the CMB temperature a and energy spectrum. Ωm+Ωr +ΩΛ≃Ωm +ΩΛ=1
−5 Radiation energy density is negligibly small today: Ωr∼10 Friedmann equation...
● You may also have seen the Friedmann equation in this form:
2 2 −3 −4 −2 H (t )=H (t0 )[ Ωm a +Ωr a +ΩΛ +ΩK a ]
2 ¯ρα (t0 ) 3 H (t ) K Ωα= , ρcrit (t )≡ , Ω K ≡− 2 2 ρcrit (t 0 ) 8 πG a H (t0 )
Critical density ● Current observations:
I'll tell you how Ωm∼0.3, ΩΛ∼0.7, |Ω K|<0.01 e.g., Ade et al. you measure −1 −1 [Planck collaboration] these in a bit... arXiv:1502.01589 H 0≡H (t 0)∼70 km s Mpc
Open, flat, K = 0 Λ-dominated
Open, curved, K = -1 Our universe! Matter-dominated
Scale factor a(t) Open, flat, K = 0 Matter-dominated
Closed, curved, K = +1 Matter-dominated
Time t 2. The hot universe and the relic neutrino background...
The hot universe...
● The early universe was a very hot and dense place.
→ Frequent particle interactions.
● If the interaction rate (per particle) is so large that
Interaction rate Γ >> Expansion rate, H
→ the interaction process is in a state of equilibrium.
Equilibrium... −5 −2 G F∼10 GeV 19 mpl∼10 GeV ● Consider the weak interaction. The interaction rate per particle is: Fermi constant Number density n ~ T 3
2 5 3 Γ=n⟨σ v⟩∼G T 2 3 T F Γ ∼m G T ∼ H pl F (1 MeV ) T = 2 2 temperature Cross section σ ~ GF T Relative velocity v ~ 1
● The Hubble expansion goes like → When the temperature exceeds O(1) MeV, even 2 weak interaction processes 8πG T are in a state of equilibrium! H = ∑ ρα∼ 3 α m √ pl Natural units k =1 Planck mass B Weak EM log(ρ) Radiation domination Matter domination Λ domination
Big bang nucleosynthesis Last scattering surface (CMB)
−4 ρr ∝a −3 Structure ρ ∝a Matter-radiation formation m equality Matter-Λ equality Today ρΛ=const
-9 -6 -3 0 log(a) redshift z a =1 By convention time t 0 g* for the standard model of particle physics:
Weak interaction goes out of equilibrium Nucleosynthesis starts
Electroweak What's left? g* (T ) phase transition Mainly ● Photons ● Neutrinos Energy density Quark-hadron normalised to the phase transition Small numbers* of photon energy density ● Electrons in one polarisation state ● Nucleons ● Nuclei
* Small means −9 <10 nγ Photon temperature Time Particle content & interactions at 0.1 < T < 100 MeV...
● QED plasma ● 3 families of neutrinos + antineutrinos + - e ,e , γ ν e ,ν¯e , ν μ , ν¯μ , ν τ , ν¯τ
EM interactions: Weak interactions @ T > O(1) MeV:
+ - + - e e ↔ e e ν i ν j ↔ ν i ν j e e↔ e e Coupled ν i ν¯j ↔ ν i ν¯j γ e↔ γ e ν i ν i ↔ ν i ν i + - γ γ ↔e e ν i ν¯i ↔ ν j ν¯j etc . ν e ↔ ν e etc . 2 5 + - Γ∼GF T ν ν¯ ↔ e e 2 Weak interactions @ T > O(1) MeV: H ∼T /mpl Particle content & interactions at 0.1 < T < 100 MeV...
● QED plasma ● 3 families of neutrinos + antineutrinos + - e ,e , γ ν e ,ν¯e , ν μ , ν¯μ , ν τ , ν¯τ
EM interactions: Weak interactions @ T > O(1) MeV:
+ - + - e e ↔ e e ν i ν j ↔ ν i ν j e e↔ e e Decoupled ν i ν¯j ↔ ν i ν¯j γ e↔ γ e ν i ν i ↔ ν i ν i + - γ γ ↔e e ν i ν¯i ↔ ν j ν¯j etc . ν e ↔ ν e etc . 2 5 ν ν¯ ↔ e+ e- Γ∼GF T Not efficient 2 Weak interactions @ T > O(1) MeV: H ∼T /m pl T< O(1) MeV Thermal history of neutrinos...
Events
Time
Photon temperature, T γ
Neutrino temperature
Phase space density
Thermal history of neutrinos...
Events Neutrinos in thermal contact with QED plasma
2 5 Weak interaction: ~G F T T 2 H Expansion rate: H ~ mplanck Time
Photon temperature, T γ 1 MeV
Neutrino temperature T =T
1 Phase space f E≃ density Relativistic Fermi-Dirac exp[ p /T ] 1 Thermal history of neutrinos...
Events Neutrinos in thermal contact g n i l with QED plasma o p n i u r t o u c e
2 5 e
Weak interaction: ~G F T N d T 2 H Expansion rate: H ~ mplanck ~H H ⇒ No thermal contact Time
Photon temperature, T γ 1 MeV
Neutrino temperature T =T
1 Phase space f E≃ density Relativistic Fermi-Dirac exp[ p /T ] 1 Thermal history of neutrinos... - + e e →γ γ becomes
n “one-way” o g Events Neutrinos in thermal contact i t n i a l o l
with QED plasma i p n i h i u r t n o u n c e a 2 5 e
- Weak interaction: ~G F T N d e + T 2 H e Expansion rate: H ~ mplanck ~H H ⇒ No thermal contact Time
Photon temperature, T γ 1 MeV 0.2 MeV
1 /3 Neutrino 4 T =T T = T temperature 11 1 Phase space f E≃ density Relativistic Fermi-Dirac exp[ p /T ] 1 g* for the standard model of particle physics: This drop here.
Weak interaction goes out of equilibrium Nucleosynthesis starts
Electroweak What's left? g* (T ) phase transition Mainly ● Photons ● Neutrinos Energy density Quark-hadron normalised to the phase transition Small numbers* of photon energy in one ● Electrons polarisation state ● Nucleons ● Nuclei
* Small means −9 <10 nγ Photon temperature Time Thermal history of neutrinos... - + e e →γ γ becomes
n “one-way” o g Events Neutrinos in thermal contact i t n i a l o l
with QED plasma i p n i h i u r t n o u n c e a 2 5 e
- Weak interaction: ~G F T N d e + T 2 H e Expansion rate: H ~ mplanck ~H H ⇒ No thermal contact Time
Photon temperature, T γ 1 MeV 0.2 MeV
1 /3 Neutrino 4 T =T T = T temperature 11 1 Phase space f E≃ density Relativistic Fermi-Dirac exp[ p /T ] 1 Comoving entropy density & its conservation...
● In a universe that expands quasi-statically (so that equilibrium is always maintained), the comoving entropy denisty S is approximately conserved.
3 ρ i+ Pi S ≡a ∑ Comoving entropy density i T i S S S
scale factor a Entropy conservation after neutrino decoupling...
QED plasma 3 families of neutrinos + antineutrinos + - e ,e , γ Same temperature ν e ,ν¯e , ν μ , ν¯μ , ν τ , ν¯τ pre-e+e- anniliation 11 7 S = π 2 T 3 a3 S = π 2 T 3 a3 e γ 45 γ ν 30 ν Pre-e+e- annihilation Conservation of S across the + - eγ Post-e e annihilation annihilation era gives: γ 4 1/3 T ν= T γ 4 2 3 3 ( 11) S e γ = π T γ a 45 4/3 Energy density per 7 4 ρ ν = ρ γ neutrino family 8 ( 11) Time Effective number of neutrinos Neff...
● It is convenient to express the neutrino energy density relative to the
photon energy density in terms of the Neff parameter:
4/3 “Standard” energy Total energy 7 4 density per flavour density in ρ ν ≡N eff × ρ γ assuming the “standard” neutrinos ∑ i i [ 8 ( 11) ] neutrino temperature
● In the idealised scenario just discussed:
by definition N eff =3
Two small corrections...
… make the neutrinos a little more energetic than is implied by N = 3. eff
● Finite-temperature QED
● Non-instantaneous neutrino decoupling
Finite-temperature QED...
● Interactions in the QED plasma cause its thermodynamical properties to deviate from an ideal gas description.
● Lowest-order O(e2) correction to the QED partition function:
Finite-temperature QED...
Ideal gas
γ e e e γ γ
γ e e γ γ e
Energy = kinetic energy + rest mass
Pressure = from kinetic energy
Finite-temperature QED...
Ideal gas + EM interactions
γ γ e e e e Temperature e e -dependent γ γ γ γ dispersion relation
γ γ e e e e γ γ γ γ e e
Energy = kinetic energy + rest mass Energy = modified kinetic energy + T-dependent masses Pressure = from kinetic energy Pressure = from modified kinetic energy
Modified QED equation of state Finite-temperature QED...
Ideal gas + EM interactions
γ γ e e e e Temperature e e -dependent γ γ γ γ dispersion relation + Forces γ γ e e e e γ γ γ γ e e
Energy = kinetic energy + rest mass Energy = modified kinetic energy + T-dependent masses + interaction potential energy Pressure = from kinetic energy Pressure = from modified kinetic energy + EM forces
Modified QED equation of state Leading-order O(e2) correction f f e N n i e g n a h 3
C + O(e ) correction (Debye-screened EM forces)
Neutrino decoupling temperature Bennett, Buldgen, Drewes & Y3W, coming to arXiv soon Two small corrections...
… make the neutrinos a little more energetic than is implied by N = 3. eff
● Finite-temperature QED
● Non-instantaneous neutrino decoupling
Non-instantaneous decoupling...
● Neutrino decoupling and electron/positron annihilation occur at similar times (T ~ 1 MeV vs T ~ 0.2 MeV). Decoupling T ~ 1MeV – Neither event is exactly localised in time.
– Some neutrinos are still decoupled to the e+e- annihilation QED plasma when the annihilation T ~ 0.2 MeV happens.
→ Neutrinos at the high energy tail (where the interaction cross-section is larger) are affected by the entropy released in the annihilation. Time ● To track the neutrino decoupling process properly through the annihilation era, we need to use the Boltzmann equation:
∂ f Phase space density 1 =−{ f 1 , H }+C [ f 1 ] Collision term of particle species 1 ∂t Hamiltonian for particle propagation
where the collision term for, e.g., 1+2 → 3+4 is Energy-momentum Matrix 9D phase space integral conservation element 4 3 1 d pi 4 4 2 C [ f 1 ]= ∫∏ 3 (2 π ) δ (P1+ P 2−P3−P 4)|M| 2 E 1 i=2 (2 π ) 2 E i
× f 3 f 4 (1± f 1)(1± f 2)− f 1 f 2(1± f 3)(1± f 4)
Quantum statistical factors ● To track neutrino oscillations too, we need to promote the classical Boltzmann equation for the phase space density to a quantum kinetic equation for the density matrix of the neutrino ensemble:
∂ f Boltzmann 1 =−{ f , H }+C [ f ] ∂t 1 1
∂ρ^ 1 QKE =− [ρ^ , H^ ]+C^ [ρ ] ∂t i ℏ Collision term
Density matrix Hamiltonian m 0 0 ∣ν e 〉 〈 ν e∣ ∣ν e 〉 〈 ν μ∣ ∣ν e 〉 〈 ν τ∣ 1 ^ 1 † ^ ρ^ = ∣ν 〉 〈 ν ∣ ∣ν 〉〈 ν ∣ ∣ν 〉 〈 ν ∣ H = U 0 m 0 U +V m μ e μ μ μ τ 2 p 2 (∣ν τ 〉 〈 ν e∣ ∣ν τ 〉 〈 ν μ∣ ∣ν τ 〉 〈 ν τ∣) ( 0 0 m3) Diagonal ~ number densities Vacuum + matter effects Off-diagonal ~ coherence Neutrino phase space distribution after e+e- annihilation
Real νe
Real νμ,τ Relativistic FD
10× f
From S. Pastor % change in the neutrino energy densities
de Salas & Pastor 2016 Add neutrino oscillations too...
● Allowing neutrinos to oscillate tends to even out the energy increase in each neutrino flavour.
The bottom line re the standard-model Neff...
● The standard-model prediction (including non-instantaneous decoupling, neutrino oscillations, and finite-temperature QED) is:
N eff =3.044→3.046
● Known to 3 significant digits. – The 4th significant digit depends on how exactly each of the afore-mentioned effects have been handled. – Still some tweaking to do!
3. Measuring the relic neutrino
background via Neff...
Direct detection of relic neutrinos...
cf WIMP detection, … is a difficult business. ~ 10-46 cm2 2 2 2 G F mν −56 mν 2 ● Small interaction cross-section: σ ∼ ≃10 cm ν N π ( eV )
● Neutrino energy too small to cross −3 most detection thresholds. p~m vearth ≃10 m
– Conventional WIMP detection techniques via nuclear recoil Speed of Earth with respect to don't work here. the CMB, ~ 370 km s-1
A zero threshold process?
● One unique candidate here...
Direct detection by neutrino capture... Weinberg 1962
β-decay end-point spectrum
- 1. N → N '+e +̄νe Cν B - 2. νe +N → N ' +e Always allowed if mν+mN >mN ' +me m u
r Local neutrino overdensity t c
e nν p Monochromatic signal from Rate∼7.5 / year / (100 g tritium) s
t relic neutrino capture ( n ) ̄ν n i o
p KATRIN
- ∼0.1 mg tritium d n e
y a c e
d 2m
- ν β Electron energy
Qβ−mν Qβ≡mN −m N ' Qβ +mν Neutrino capture with KATRIN... Kaboth, Formaggio & Monreal 2010
Requires a 109 local overdensity of neutrinos in a 3-year run for a 90% C.L. detection.
106 CνB events/yr 0 CνB events/yr
Neutrino clustering onto the Galactic halo
Expected background ~ 10 mHz
Realistic local neutrino overdensity... Ringwald & Y3W 2004
Solar system
Neutrino mass y t i s n e d r e v O
Distance from Galactic centre The bottom line:
Direct detection of the relic neutrinos is not going to happen anytime soon…
… but there are other ways to establish their presence...
Indirect evidence for relic neutrinos...
● Light element abundances
● CMB anisotropies
State-of-the-art: Temperature and polarisation fluctuations in the cosmic microwave background as seen by Planck. (Latest results 2018.)
Temperature
Polarisation TT (temperature auto-correlation)
TE EE (cross-correlation) (E-mode polarisation auto-correlation)
Ade et al. [Planck collaboration] 2015 CMB anisotropies are sensitive to Neff too...
● At the most basic level, changing the neutrino energy density shifts the epoch of matter-radiation equality. log( ρi) Radiation: −4 R∝a −1 Equality zeq≡aeq −1≈1000 Matter: −3 M ∝a Vacuum energy: BBN ρ R Present a=1; z=0 ∝const Last scattering ρM surface (CMB)
-4 0 log(a) redshift z z redshift z time But it's not as simple as that...
● Neff looks easy to detect in the CMB TT spectrum.
● But we also use the same data to measure at least 6 other parameters:
Hubble parameter baryon density
(ωb ,ωm ,h , As , ns ,τ)
matter density optical depth to reionisation primordial fluctuation amplitude & spectral index
Figure courtesy of J. Hamann ● Plenty of parameter degeneracies! What the CMB really probes: equality redshift...
Exact degeneracy between the physical matter density ω and N . Ratio of 3rd and 1st peaks sensitive to the m eff
redshift of matter-radiation equality via the ωm ωm 1 1+ zeq = ≃ early ISW an other time-dependent effects. ωr ωγ 1+ 0.2271 N eff
Fixed: zeq
Figure courtesy of J. Hamann What the CMB really probes: sound horizon...
Exact degeneracy between ωm and the Hubble parameter h. Peak positions depend on: −2 −1/ 2 (ω h ) Sound horizon Flat ΛCDM θ ∝ m r s 1 θ = s at decoupling da s ∫ D A Angular distance to the Fixed −2 −3 −2 z , a * √ωm h a + (1−ωm h ) last scattering surface eq ωb
Fixed: z , ω , θ Fixed: zeq eq b s
Figure courtesy of J. Hamann What the CMB really probes: anisotropic stress...
Apparent (i.e., not physical) partial ● However, free-streaming (non- degeneracies with inflationary parameters: interacting relativistic) particles have
primordial fluctuation amplitude As and anisotropic stress. spectral index n . ● First real signature of N in the 3rd s eff peak!
Fixed: z , ω , θ , A (l=200) Fixed: zeq, ωb, θs eq b s s
Figure courtesy of J. Hamann Neff signatures in the CMB damping tail...
● Measured by ACT since 2010; SPT since 2011; Planck since 2013.
● Probe photon diffusion scale:
rd Diffusion scale θd= at decoupling D A
● Primary signature of Neff in the Planck era.
Hou, Keisler, Knox et al. 2011 Aghanim et al. [Planck] 2018 Current constraints on Neff ... Ade et al. [Planck] 2015
Planck-inferred Neff compatible with 3.046 at better than 2σ.
ΛCDM+Neff Planck 2018 (95%) Planck2015 (95%) 7-parameter fit TT+lowE +0.57 3.13±0.64 3.00 -0.53 +lensing+BAO +0.44 n/a 3.11 -0.43
TT+lowE+TE+EE +0.36 2.99±0.40 2.92 -0.37
+lensing+BAO +0.34 n/a 2.99 -0.33
+0.34 95% C. L. ΛCDM+Neff+neutrino mass N eff =2.96- 0.33 Planck TT+TE+EE+lowE 8-parameter fit ∑ mν <0.12 eV +lensing+BAO
Flies in the ointment: the H0 discrepancy...
3.6σ discrepancy between the Planck- inferred H0 and local measurements:
● TT+TE+EE+lowE+lensing
−1 −1 H 0=67.36±0.54 km s Mpc
● Local measurement:
−1 −1 H 0 =73.52±1.62 km s Mpc Planck Planck+Riess18 Riess et al. 2018
Joint Planck+Riess 2018 fit varying Neff: N =3.27±0.15 68% C. L. eff Planck TT+TE+EE+lowE −1 −1 H 0 =69.32±0.97 km s Mpc +lensing+BAO+Riess Take-home message...
● The prediction of a relic neutrino background is as fundamental as the prediction of the CMB.
● Direct detection based on scattering seems impossible at the moment...
● However, we can establish the CνB's presence through its effects on
– The light elemental abundances
– The CMB temperature anisotropies
→ The Planck measurements are consistent with N = 3. eff
→ However, a 3.6σ discrepancy between Planck and local measurements
of H0 remains in ΛCDM, which cannot be resolved with Neff>3. The
discrepancy does however drive up slightly the preferred value of Neff in a combined analysis. Extra slides...
Primordial light elements...
Big bang nucleosynthesis...
● The production of light nuclei at temperatures: T ∼O(100)→O(10) keV – Deuterium, Helium-3, Helium-4, Lithium-7, etc.
● A 2-parameter problem: The initial neutron-to-proton ratio. Relic neutrinos affect mainly this
The baryon-to-photon ratio; determines when the production of the first nucleus in the chain, Deuterium, should begin. Relevant temperatures: Setting the n/p ratio... T ~ 0.8 → 0.1 MeV
● At T > 1 MeV the neutron- to-proton ratio is set by the interactions: + ̄νe+ p → e +n − νe+n → e + p n m −m ≃exp − n p ( p ) T eq ( γ )
● After freeze-out neutron decay can still change the n/p ratio: Freeze-out, i.e., Scattering rate per particle < Hubble expansion rate τn =885.6±0.8 s
Relic neutrinos and the n/p ratio... Photons and neutrinos dominate the energy density at the time ● Hubble expansion rate: of nucleosynthesis 1 d a 2 8π G 8 πG H 2= = ρ ≃ (ρ + ρ ) ( ) total γ ∑ ν, i a d t 3 3 i Total energy density: radiation, matter vacuum energy...
→ The higher the neutrino energy density the earlier the freeze-out (and vice versa) → Higher n/p ratio:
n mn −m p ≃exp − p freeze T freeze Freeze-out temperature The n/p ratio affects all light elemental abundances.
n pe − e e p e n − e n e p − n p e e
Freeze-out
Measuring primordial abundances...
● Light element abundances we observe in astrophysical systems today are generally not at their primordial values.
Deuterium Destroyed in stars. Data from high-z, low metallicity QSO absorption line systems Helium-3 Produced and destroyed in stars. Data from solar system and Complicated evolution. galaxies, but not used in BBN analyses. Helium-4 Produced in stars by H burning. Data from low metallicity, extragalactic HII regions. Lithium-7 Destroyed in stars, produced in Data from the oldest, most metal cosmic ray interactions. poor stars in the Galaxy.
● For measurements, low metallicity systems with as little evolution as possible are the best bets!
Light element constraints on Neff... s o n i r t u e
n N = 3 is consistent
eff f o
with measurements. r e b m u n Helium-4 e v i t c e f f E m teriu Deu
Baryon density Ade et al. [Planck] 2016 Light element constraints on Neff... 5 4 0 . 3 N = 3 is consistent
− eff f f e with measurements. N =
ν N Δ
Riemer-Sørensen Baryon-to-photon ratio & Jenssen 2017 Planck CMB: flies in the ointment...
Small fly: the σ8-Ωm discrepancy...
Cosmic shear measurements tend to prefer lower values of σ8 or Ωm than Planck.
● Mostly mild to modest discrepancy
● (One claim of 2.6σ discrepancy from KiDS Joudaki et al. 2018)
● Appears amenable to improved treatment of lensing systematics.