Neutrinos in cosmology - INDICO (Indico)...species by number density. Light neutrinos (m < eV)...

Neutrinos in cosmology

Yvonne Y. Y. WongRWTH Aachen

INSS 2012, Blacksburg VA, July 10 – 21, 2012

BBN

Structureformation

Last scatteringsurface (CMB)

Inflation: seedsfor structureformation?

BBN

Structureformation

Last scatteringsurface (CMB)

Inflation: seedsfor structureformation?

Why study neutrinos??

Big bang neutrinos are the second most abundant known particle species by number density.

Light neutrinos (m < eV) behave as:● Radiation at early times (BBN).● Matter at late times (structure formation).

● Lecture 1: Neutrinos and homogeneous cosmology

– Homogeneous and isotropic universe

– Particles in cosmology: the hot universe

– Evidence for relic neutrinos

– Prospects for direct detection

● Lecture 2: Neutrinos in the inhomogeneous universe

Plan...

● J. Lesgourgues and S. Pastor, Massive neutrinos and cosmology, Phys. Rep. 429 (2006) 307 [astro-ph/0603494].

● S. Hannestad, Primordial neutrinos, Ann. Rev. Nucl. Part. Sci. 56 (2006) 137 [hep-ph/0602058].

● Y. Y. Y. Wong, Neutrino mass in cosmology: status and prospects, Ann. Rev. Nucl. Part. Sci. 61 (2011) 69 [arXiv:1111.1436].

● A. D. Dolgov, Neutrinos in cosmology, Phys. Rept. 370 (2002) 333 [hep-ph/0202122].

Useful references...

1. Neutrinos and homogeneous cosmology...

1.1 Homogeneous and isotropic universe...

● Modern cosmology is based on the hypothesis that our universe is homogeneous and isotropic on sufficiently large length scales.

– Homogeneous → same everywhere

– Isotropic → same in all directions

– Sufficiently large scales → > O(100 Mpc)

● I pc = 1 parsec = 3.0856 x 1018 cm

– Distance from Sun to Galactic centre ~ 10 kpc

– Distance to the Virgo cluster ~ 20 Mpc

– Size of the visible universe ~ O(10 Gpc)

Friedmann-Lemaître-Robertson-Walker universe...

● Homogeneity and isotropy imply maximally symmetric 3-spaces (3 translational and 3 rotational symmetries).

– A spacetime metric that satisfies these requirements:

Friedmann-Lemaître-Robertson-Walker universe...

ds2=−dt 2+a2(t)[ dr21−K r2+r2(d θ2+sin2θd ϕ2)] FLRW metrica(t) = Scale factor

Spatial geometryK = -1 (hyperbolic), 0 (flat), +1 (spherical)

● Test particles moving on geodesics in a FRLW universe suffer cosmological redshift:

● For photons:

● In a FRLW universe, there is a one-to-one correspondence between t, a, and z → We use them interchangeably as a measure of time.

Kinematics: cosmological redshift...

∣⃗p∣∝a−1Proper momentum of a point particle measuredby a comoving observer

λ0λe=E eE0=a ( t0)a (te)

≡1+zz = Redshift parameter

Wavelength measured by comoving observer

Wavelength emittedby comoving emitter

t0= today

● Matter/energy content is encoded in the stress-energy tensor Tμν.

● Homogeneity and isotropy imply only one viable form:

– Fluids at rest with respect to the FLRW coordinates (or comoving frame)

Matter/energy content...

T̄ (α)μ ν=(−ρ̄α(t) ḡ 00 00 P̄α(t) ḡ ij)

ρα = Energy density of fluid α in the fluid's rest frame

Pα = Pressure of fluid αin the fluid's rest frame

● Relativistic (at least for a significant part of their evolution history

– Photons (mainly the CMB)– Relic neutrinos (analogous to the CMB)– Gravitational waves??

● Nonrelativistic matter– Atoms (or constituents thereof)– Dark matter (does not emit light but feels gravity)

● Other funny things

– Vacuum energy/dark energy– ??

Matter/energy content: what is out there?

● Local conservation of energy-momentum:● In a FLRW universe:

● A general fluid can be specified by an equation of state parameter:

– Nonrelativistic matter (wm ~ 0):

– Radiation (wr = 1/3):

– Vacuum energy (wΛ = -1):

Matter/energy content: conservation laws...

∇μT (α)μν=0

d ρ̄αdt +3

ȧa (ρ̄α+P̄α)=0

Continuity equation;one equation per fluid α

ρ̄m∝a−3

ρ̄r∝a−4

ρ̄Λ∝constant

wα( t )≡ P̄α( t )/ρ̄α(t)

log(ρ)

log(a)

ρ̄r∝a−4

ρ̄Λ=const

ρ̄m∝a−3

Radiation domination Matter domination Λ domination

Matter-radiationequality

Matter-Λequality

log(ρ)

log(a)-3 0

ρ̄r∝a−4

ρ̄Λ=const

-9 -6

ρ̄m∝a−3



Matter-Λequality

Today

a0=1 By convention

log(ρ)

log(a)-3 0

ρ̄r∝a−4

ρ̄Λ=const

-9 -6

ρ̄m∝a−3



Matter-Λequality

Today

a0=1 By convention

Structure formation

Last scattering Surface (CMB)

Big bangnucleosynthesis

13.4 billion years ago(at photon decoupling)

Composition today

● Different evolution for different forms of energy densities means that radiation dominated in the early universe, while dark energy was relatively unimportant.

MasslessNeutrinos(3 families)

● Derived from the Einstein equation:

● The Friedmann equation is an evolution equation for the scale factor a(t):

● Friedmann+continuity equations → specify the whole system.

Friedmann equation...

H 2(t)≡( ȧa )2

=8πG3 ∑α ρ̄α−K

Friedmann equation

Rμν−12gμνR=8πGT μν

H(t) = Hubble parameter

● You may also have seen the Friedmann equation in this form:

● Current observations:

Friedmann equation: critical density...

H 2(t)=H 2(t 0)[Ωma−3+Ωra−4+ΩΛ+ΩK a−2 ]

Ωα=ρ̄α(t 0)ρcrit( t0)

, ρcrit(t )≡3H 2(t )8πG , ΩK≡−

Ka2( t0)H

2(t 0)

Ωm∼0.3, ΩΛ∼0.7, Ωr∼10−5

∣ΩK∣

● Solutions in some limits:

– Radiation domination:

– Matter domination:

– Vacuum energy domination:

Friedmann equation: solutions...

a∝ t1 /2

a∝ t 2/3

a∝exp(H 0√ΩΛ t)

1.2 Particles in cosmology: the hot universe...

● The early universe was a very dense and hot place.

→ Frequent particle interactions.

● If the interaction rate is so large

such that

→ the interaction is in a state of equilibrium.

The hot universe...

Interaction rate, Γ >> Expansion rate, H

=n 〈 v〉

● When an interaction is in a state of equilibrium, all participating particles have phase space distributions described by one of the equilibrium forms.

– All scattering processes lead to kinetic/thermal equilibrium:

– Annihilation processes XX ↔ YY ↔ γγ lead to chemical equilibrium:

f eq( p)=1

exp [(E ( p)−μ)/T ]±1

X=− X

+ Fermi-Dirac- Bose-Einstein

μ = Chemical potential

f(p) = Phase space distribution

Equilibrium thermodynamics...

Same temperature for all participating particle species

● Number density:

● Energy density:

● Pressure:

ρ= g(2π)3

∫ d 3 pE f ( p⃗)

n= g(2π)3

∫ d 3 p f ( p⃗) g = Internal d.o.f. = 2 for neutrinos

P= g(2π)3

∫ d 3 p∣p⃗∣2

3Ef ( p⃗)

Compare with g = 4 for electrons/positrons = 2 for photons

Relativistic Non-Bose Fermi relativistic

Number density, n:

Energy density, ρ:

Pressure, P:

32

g T 3 g mT2 3/2

e−m /T3432

gT 3

2

30g T 4 7

82

30gT 4 mn

132

30g T 4 1

3782

30gT 4 negligible

Assuming T >> μ

● As the temperature drops, some interactions become unable to keep up with the expansion.

→ These interactions falls out of equilibrium, i.e., they freeze out.

● A rough “out-of-equilibrium” condition:

● Particle species is decoupled when all of its interactions satisfy this condition, because then it has no more thermal contact with other particle species in the universe.

Interaction rate, Γ

● At temperatures O(1) < T < O(100) MeV, weak interactions keep neutrinos coupled to other particles in the thermal bath:

– Weak interaction rate:

– Hubble expansion rate:

● When the weak rate drops below the Hubble expansion rate, the neutrinos lose thermal contact with other particles → neutrinos decouple.

Neutrino decoupling

Γ=σ νe ne∼G F2 T 5

H=√ 8πG3 ∑i ρ̄i∼ T2

mpl

ν+ e↔ν+ e , ν ν̄↔e+ e-

T νdec∼1 MeV Neutrino decoupling temperature

Time

Photon temperature, Tγ

Events

Neutrino temperature

Phase spacedensity

Thermal history of neutrinos...

T =T

Time

Photon temperature, Tγ

~GF2 T 5

H~ T2

mplanck

Weak interaction:

Expansion rate:H

Neutrinos in thermal contact with cosmic plasma

Events


Phase spacedensity Relativistic Fermi-Dirac


1 MeV

f E≃1

exp [ p /T ]1

T =T

Time

Photon temperature, Tγ 1 MeV

Neu

trino

deco

uplin

g

~GF2 T 5

H~ T2

mplanck

Weak interaction:

Expansion rate:H

H ⇒~H


Events


Phase spacedensity

No thermal contact

Relativistic Fermi-Dirac


f E≃1

exp [ p /T ]1

T =T T = 411 1 /3

T

Time

Photon temperature, Tγ 1 MeV 0.2 MeV

Neu

trino

deco

uplin

g

~GF2 T 5

H~ T2

mplanck

Weak interaction:

Expansion rate:

e+e-

ann

ihila

tion

HH ⇒~H


Events


Phase spacedensity

No thermal contact

Relativistic Fermi-Dirac


f E≃1

exp [ p /T ]1

e-e+→γ γbecomes “one-way”

● Before annihilation: Entropy mainly from: photons, electrons/positrons, and neutrinos.

● After annihilation: Entropy from photons and (colder) neutrinos:

● Using

s a1=4390

2T 3 a1

s a2=22

45 [2T 3 a2 78 6T 3 a2]a1

3 s a1=a 23 s a2 ; a1T a1=a2T a2

T = 411 1 /3

T Neutrino temperatureafter annihilation

s≡∑i

iPiT i

∝a−3Entropy

Neutrino temperature...

● Neutrino decoupling and electron/positron annihilation occur at similar times (T ~ 1 MeV vs T ~ 0.2 MeV).

– Some neutrinos are still decoupled to the plasma when the annihilation happens.

→ Neutrinos at the high energy tail are affected by the entropy released in the annihilation.

– Expect neutrinos to be a little hotter than .

Non-instantaneous decoupling...

T = 411 1 /3

T

● To track the decoupling and reheating processes properly, we use the Boltzmann equation.

● Suppose we have a process:

● Then:

d f 1 p , t d t

= 12 E1∫∏

i=2

4 d 3 pi23 2 E i

244P1P2−P3−P4∣M∣2

× f 3 f 41± f 11± f 2− f 1 f 2 1± f 31± f 4

1234

9D phase space Energy-momentumconservation Matrix element

Phase space density of 1

Statistical factors+ for boson- for fermion

From S. Pastor

10× f

Relativistic FD

Real νµ,τ

Real νe

Neutrino phase space distribution after e+e- annihiliation

● It is convenient to express the increase of neutrino energy density in terms of an increase in the effective number of neutrino families:

∑ii≡N eff× , 0

“Standard” energy density per flavourassuming the “standardneutrino temperature

Total energy density in neutrinos

N eff=3.04

● Non-instantaneous decoupling and finite temperature QED effects together lead to:

● Temperature:

● Number density per flavour:

T ,0= 411 1 /3

T CMB ,0=1.95 K~10−4 eV

n ,0 =611

32

T CMB , 03 =

311nCMB ,0 = 112 cm

−3

CMB number density

TCMB,0 = 2.725 ± 0.001 K

A summary: the relic neutrino background today...

● Energy density per flavour:

● Closure bound:

Nonrelativistic= Neutrinodark matter

i≡i ,0crit , 0

; crit ,0=3H 0

2

8G

Gerstein & Zel'dovich 1966; Cowsik & McClelland 1972

ρν ,0={ 78 ( 411 )4/3

ρCMB ,0 ⇒ Ων ,0h2 = 6×10−6

mν nν ,0 ⇒ Ων ,0h2 =

mν94 eV

} m≪T ,0~10−4 eVm≫T ,0~10

−4 eV

If relativistic today

If nonrelativistic today

1 ⇒ m90 eVMore on this tomorrow

● Nonrelativistic neutrinos cluster gravitationally in dark matter halos.

– Expect mν-dependent variations in number density and phase space distribution.

Ringwald & Y3W 2004

mν =

mν =

mν =

mν =

Distance from the Galactic centre

Ove

rden

sity

nν/n

ν in

the

Milk

y W

ay

Solar system (~ 8 kpc)Local variations...

● Nonrelativistic neutrinos cluster gravitationally in dark matter halos.

– Expect mν-dependent variations in number density and phase space distribution.

Ringwald & Y3W 2004

Local variations... Rel. Fermi-DiracClustered

Pha

se s

pace

den

sity

at r

= 8

kpc

Neutrino momentum/temperature

1.3 Evidence for relic neutrinos...

● Big Bang nucleosynthesis

● Precision cosmology– Cosmic microwave background

– Large-scale structure distribution

(Indirect) evidence for relic neutrinos...

● Relevant temperatures:

● Production of

– Deuterium

– Helium-3

– Helium-4

– Lithium-7

– small amounts of others● Two phases

Big Bang nucleosynthesis...

T~O 100O 10 keV(after neutrino decoupling)

Phase 1: Setting the n/p ratio...

e p en

en e− p

n=885.6±0.8 s

● At T > 1 MeV the neutron-to-proton ratio is set by the interactions:

● After freeze-out neutron decay can still change the n/p ratio:

np eq≃exp −mn−mpT

Freeze-out

Relevant temperatures:T ~ 0.1 → 0.01 MeV

Phase 2: Formation of nuclei... Relevant temperatures:T ~ 0.1 → 0.01 MeV

● Beginning with Deuterium.

● Starting time set by the baryon-to-photon ratio η.

– Large entropy (small η) leads to the destruction of nuclei by photo-disintegration.

● The rest is governed by (known) nuclear physics.

→ Standard BBN has only one free parameter, η.

Standard BBN predictions as functions of the baryon-to-photon ratio η

Deuterium Destroyed in stars. Data from high-z, low metallicity QSO absorption line systems

Helium-3 Produced and destroyed in stars. Complicated evolution.

Data from solar system and 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 cosmic ray interactions.

Data from the oldest, most metal poor stars in the Galaxy.

Measuring primordial abundances...

● Light element abundances we observe in astrophysical systems today are generally not at their primordial values.

● For measurements, low metallicity systems with as little evolution as possible are the best bets!

● Neutrinos affect Phase 1 of BBN through the interactions:

● Two ways:

– Change the freeze-out termpature of the interactions.

– Directly affect the weak interaction rates.

e p en

en e− p

Neutrinos and BBN... ...One

● Expansion of the universe described by the Friedmann equation:

● At and before the time of nucelosynthesis, radiation dominates energy density:

ρtotal≃ργ+∑iρν , i=ργ+N eff ρν

H 2=(1a d ad t )2

=8πG3

ρ total

Effective number of thermalised neutrinospecies

Energy density inone thermalisedneutrino species

First effect: freeze-out time

Total energy density:radiation, mattervacuum energy...

Photons

N eff=3.04Standard:

e p en

en e− p

● Increasing Neff raises the freeze-out temperature and hence the neutron-to-proton ratio:

np freeze≃exp −mn−m pT freeze Freeze-out

Helium-4 is most sensitive to Neff...

e p e n

en e− p

n p e − e

● Nearly all neutrons end up in Helium-4.

∣Y He≡4nHenN ≈ 2n / p1n / p∣t BBNHelium-4 mass fraction ~ 0.25for n/p ~ 1/7

Freeze-out

n pe − e

Depends onexpansion rate,and hence Neff

N eff=4

N eff=3

N eff=2

Baryon-to-photon ratio

Hel

ium

-4 a

bund

ance

Helium-4 is most sensitive to Neff...

Strumia & Vissani 2006

Neff

Helium-4 mass fraction, YHe

Time

BBN prefers Neff > 0.

Neff = 3

He-4 measurements in low metallicityextragalactic HII regions

● Recent analyses suggest a mild preference for Neff > 3 (or Ns > 0) from the Deuterium+Helium-4 abundance.

Evidence for Neff > 3 from BBN??

τn=878.5sτn=885.7s+ CMB prior onbaryon density

Hamann, Hannestad, Raffelt & Y3W 2011

● Neutrinos affect Phase 1 of BBN through the interactions:

● Two ways:

– Change the freeze-out termpature of the interactions.

– Directly affect the weak interaction rates.

e p en

en e− p

Neutrinos and BBN... ...Two

● Electron neutrinos affect directly the interactions:

before the interactions freeze out.

● In the standard model, neutrinos and antineutrinos have the same abundance.

– If there is an asymmetry in the neutrino and antineutrino number densities, it will affect the neutron-to-proton ratio primarily through these interactions.

Second effect: weak interaction rate

e p en

en e− p

● Neutrino-anitneutrino asymmetries are usually parameterised in terms of a finite chemical potential in the equilibrium phase space distribution:

● Effects on the neutron-to-proton ratio:

– i.e., a large asymmetry in the electron neutrinos drives down n/p.– Current constraint:

np≈exp [−mn−mpT − e] , ≡T

f e E =1

exp [ p−/T ]1, f eE =

1exp[ p /T ]1

Neutrinos Antineutrinos

µ = Chemical potential

e0.1 e.g., Raffelt & Serpico 2004

Assuming chemcialequilibrium holds

ξ = Degeneracy parameter

● BBN is also sensitive to neutrino-antineutrino asymmetries in the muon and tau neutrino sector, because:

– A large lepton asymmetry also contributes to the energy density:

– More importantly, flavour oscillations equilibrate all asymmetries prior to weak freeze-out.

A large lepton asymmetry in νμ,τ?

N eff=3+∑i[ 307 ( ξνiπ )

2

+157( ξνiπ )

4]

Dolgov et al. 2002Y3W 2002Abazajian et al. 2002

e. ,0.1

Bound on applies to all neutrino flavours!

e

time

Che

mic

al p

oten

tial ντ

νµ

νe

1. νμ ↔ ντ equilibration at T ~ 10 MeV.

2. νe ↔ νμ,ντ equilibration at T ~ 2 – 3 MeV.

BBN

matm2 ,atm msun

2 ,sun

● Big Bang nucleosynthesis

● Precision cosmology– Cosmic microwave background

– Large scale structure distribution

(Indirect) evidence for relic neutrinos...

Precision cosmological probes

Cosmic microwave background

CMB temperature anisotropy spectrum

Galaxy clustering

Lyman-α forest

Gravitationallensing

Cluster abundance

Precision cosmological probes

Large-scale structure distribution

Matter power spectrum

● For CMB and LSS, the main role of relic neutrinos is to fix the epoch of matter-radiation equality.

log(ρ)

log(a)

ρ̄Λ=const

ρ̄m∝a−3



Matter-Λequality

aeq

ρ̄r∝a−4

CMB TT

● CMB: Delaying matter-radiation equality enhances the first peak of the temperature anisotropies relative to the plateau via the early Integrated Sachs-Wolfe (ISW) effect.

● Sachs-Wolfe effect:

ObserverRedshift

Ψ=0

Gravitational potential Blueshift

Observed temperature fluctuation

ΔTT observed

=ΔTT intrinsic

+Ψ

Ψ

● Integrated Sachs-Wolfe (ISW) effect:

● Except during matter domination, gravitational potentials decay with time.

→ Photons suffer less redshift than in the case of constant Ψ → Larger observed temperature fluctuations.

ObserverRedshift

Observer

time

Ψ=0

Gravitational potential

● LSS: Delaying matter-radiation equality shifts the turning point of the matter power spectrum to a smaller k (larger comoving Hubble radius at equality).

N eff=1 ,3 ,5 ,7 ,9

Large-scale structure

k eq=4.7×10−4√Ωm(1+ zeq)hMpc−1

● Recent CMB+LSS data appear to prefer Neff > 3!

Dunkley et al. [Atacama Cosmology Telescope] 2010 Keisler et al. [South Pole Telescope] 2011

WMAP+ACTWMAP+ACT+H0+BAO

WMAP

Stan

dard

val

ue

Stan

dard

val

ue

Evidence for Neff > 3 from CMB+LSS??

● Neff>3 trend has been there since WMAP-5.

● Exact numbers depend on the cosmological model, and the combination of data.

● Many model+data combinations find Neff>3 at 95% – 99% C.L.

● Central value Neff ~ 4.

W-5=WMAP-5; W-7=WMAP-7

= >95% C.L.

Abazajian et al., “Light sterile neutrinos: a white paper”, 2012

Planck and Neff...

Bashinsky & Seljak 2004Helium fractionas a free parameter

68% sensitivities

● If Neff is as large as 4, it will be settled almost immediately by Planck (launched May 14, 2009; public data release early 2013).

1.4 Prospects for direct detection...

● G. B. Gelmini, Prospects for relic neutrino searches, Phys. Scripta T121 (2005) 131 [hep-ph/0412305].

● A. Ringwald, Prospects for direct detection of the cosmic neutrino background, arXiv:0901.1529.

Useful references...

Direct detection is difficult because...

● Neutrinos interact weakly.

● Momentum transfer per scattering is too small to cross most interaction thresholds.

– A zero threshold interaction?

N~G F

2 m2

≃10−56 meV

2

cm2

p~m vearth≃10−3m

Speed of Earth wrt to the CMB,~ 370 km s-1

cf wimp detection, ~ 10-46 cm2

Neutrino-nucleoncross-section

Weinberg 1962

N N 'e − e1.

2.

3.

Assuming massless neutrinos

β-decay and related...

Qβ

Electronenergy

β-de

cay

end-

poin

t spe

ctru

m

QβQβ-EF

Weinberg 1962

N N 'e − eN N 'e − e , e

RNB~degenerate

Phase space blocking

EF = Fermi energy of degenerate relic (anti-)neutrinos

1.

2.

3.


β-decay and related...β-

deca

y en

d-po

int s

pect

rum

Electronenergy

Qβ+EF

Weinberg 1962

N N 'e − eN N 'e − e , e

RNB~degenerate

eRNBN N 'e − , e

RNB~degenerate


EF = Fermi energy of degenerate relic (anti-)neutrinos

1.

2.

3.


Capture of degeneraterelic neutrinos

β-decay and related...

QβQβ-EF

Electronenergy

β-de

cay

end-

poin

t spe

ctru

m

● In 1962, detection required:

● Present limit from BBN:

→ Impossible even for KATRIN (end-point resolution ~ 1 eV).

N N 'e − e


1.

2.

3.

S. Weinberg, Phys. Rev. 128 (1962) 1457

0.1

~EFT , 0

200 eV10−4 eV

~106

Relic neutrino temperature

Degeneracyparameter

⇒E F10−5 eV

QβQβ-mν Qβ+mν

Cocco, Mangano & Messina 2007Lazauskas, Vogel & Volpe 2007Blennow 2008

2mν

N N 'e − e e

RNBN N 'e −1.

2.

mν = Neutrino mass

Monochromatic signal from relic neutrino captureRate~6.5 nn / year / 100 g 3 H

… and a recent revival...β-

deca

y en

d-po

int s

pect

rum

Electronenergy

Lazauskas, Vogel & Volpe 2007

● The challenge: energy resolution!!!!

– Otherwise signal will be swamped by the β-decay tail.

Signal

Tritium β-decay tail folded with ∆E = 0.5 eV resolution

Fiducial mν = 1 eV

EmFor S/N > 1:

Blennow 2008

Signal vs background : fiducial mν = 0.05 eV

E=0.03 eV E=0.06 eV

⇒ S /N1⇒ S /N1

This is what it takes to get an end-point energy resolution of ~1 eV...

KATRIN main spectrometer

Summary...

● Relic neutrinos = a fundamental prediction of hot big bang theory.

● Good (indirect) evidence for their existence from BBN and CMB/LSS observations.

– Maybe there are even more than three neutrino species....

– Planck will tell!

● Direct detection (with existing technology) is still a long way away.

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Neutrinos in cosmology - INDICO (Indico)...species by number density. Light neutrinos (m < eV)...

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Transcript of Neutrinos in cosmology - INDICO (Indico)...species by number density. Light neutrinos (m < eV)...