Cosmological probes of neutrino masses (Neutrinos in Cosmology)

Lecture I

Sergio Pastor (IFIC Valencia)

INT. SCHOOL OF PHYSICSENRICO FERMI, CLXX COURSE

Varenna, June 2008

ν

Neutrinos in Cosmology

1st lecture

Introduction: neutrinos and the History of the Universe

This is a neutrino!

T~MeVt~sec

Primordial

Nucleosynthesis

Decoupled neutrinos(Cosmic Neutrino

Background or CNB)

Neutrinos coupled by weak

interactions

At

least 1

specie

s is NR

Relativistic neutrinos

T~

eVNeutrino cosmology is interesting because Relic neutrinos

are very abundant:

• The CNB contributes to radiation at early times and to matter at late times (info on the number of neutrinos and their masses)

• Cosmological observables can be used to test non-standard neutrino properties

Relic neutrinos influence several cosmological epochs

T < eVT ~ MeV

Formation of Large Scale Structures

LSS

Cosmic Microwave Background

CMB

PrimordialNucleosynthe

sis

BBN

No flavour sensitivity Neff & mννevs ν , μ τ Neff

Basics of cosmology: background evolution

Introduction: neutrinos and the History of the Universe

Relic neutrino production and decoupling

Neutrinos in Cosmology

Neutrinos and Primordial Nucleosynthesis

Neutrino oscillations in the Early Universe

Neutrinos in Cosmology

Degenerate relic neutrinos (Neutrino asymmetries)

Massive neutrinos as Dark Matter

Effects of neutrino masses on cosmological observables

Bounds on mν from CMB, LSS and other data

Bounds on the radiation content (Nν)

Future sensitivities on mν and Nν from cosmology

Suggested References

BooksModern Cosmology, S. Dodelson (Academic Press, 2003)

The Early Universe, E. Kolb & M. Turner (Addison-Wesley, 1990)

Kinetic theory in the expanding Universe, Bernstein (Cambridge U., 1988)

Recent reviewsNeutrino Cosmology, A.D. Dolgov,

Phys. Rep. 370 (2002) 333-535 [hep-ph/0202122]

Massive neutrinos and cosmology, J. Lesgourgues & SP, Phys. Rep. 429 (2006) 307-379 [astro-ph/0603494]

Primordial Neutrinos, S. HannestadAnn. Rev. Nucl. Part. Sci. 56 (2006) 137-161 [hep-ph/0602058]

BBN and Physics beyond the Standard Model, S. SarkarRep. Prog. Phys. 59 (1996) 1493-1610 [hep-ph/9602260]

Eqs in the SM of Cosmology

++

−−== 22222

2

2222 sin

1dθ φrdθr

krdr

a(t)dtdxdxgds νμμν

µνµνµνµνµν π gGTRgRG Λ+=−= 821

The FLRW Model describes the evolution of the isotropic and homogeneous expanding

Universe

a(t) is the scale factor and k=-1,0,+1 the curvature

Einstein eqs

Energy-momentum tensor of a perfect fluid

µννµµν ρ pguupT −+= )(

Eqs in the SM of Cosmology

)(3.

ppHdtd +−== ρρ

Eq of state p=αρ ρ = const a

-3(1+α)

Radiation α=1/3 Matter α=0 Cosmological constant α=-1 ρR~1/a4 ρM~1/a3 ρΛ~const

2

2.

2

38

)(akG

aa

tH −=

= ρπ00 component

(Friedmann eq)

H(t) is the Hubble parameterρ=ρM+ρR+ρΛ

1)( 22 −= Ω

atHk

ρcrit=3H2/8πG is the critical density

Ω= ρ/ρcrit

Evolution of the Universe

)3(3

4..

pG

aa +−= ρπ

accélération

accélération

décélération lente

décélération rqpide

accélération

accélération

décélération lente

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

inflation RD (radiation domination) MD (matter domination) dark energy domination

)3(3

4..

pG

aa +−= ρπ

a(t)~t1/2 a(t)~t2/3 a(t)~eHt

Evolution of the background densities: 1 MeV → now

3 neutrino species

with different masses

Evolution of the background densities: 1 MeV → now

photons

neutrinos

cdm

baryons

Λ

m3=0.05 eV

m2=0.009 eV

m1≈ 0 eV

Ωi= ρi/ρcrit

Equilibrium thermodynami

cs

Particles in equilibriumwhen T are high and interactions effective

T~1/a(t)

Distribution function of particle momenta in equilibrium

Thermodynamical variables

VARIABLERELATIVISTIC

NON REL.BOSE FERMI

T~MeVt~sec

Primordial

Nucleosynthesis

Neutrinos coupled by weak

interactions(in equilibrium)

1e1

T)(p,f p/T +=ν

-αα

-α

-α

βαβα

βαβα

ee

ee+↔

↔

↔↔

νν

νν

νννν

νννν

Tν = Te = Tγ

1 MeV ≤ T ≤ mμ

Neutrinos in Equilibrium

Neutrino decoupling

As the Universe expands, particle densities are diluted and temperatures fall. Weak interactions become ineffective to keep neutrinos in good thermal contact with the e.m. plasma

Rate of weak processes ~ Hubble expansion rate

MeV T Mπρ

T GMπρ

n , HσΓ νdec

p

RF

p

Rww 1

38

38

v 252

22 ≈→≈→=≈

Rough, but quite accurate estimate of the decoupling temperature

Since νe have both CC and NC interactions with e±

Tdec(νe) ~ 2 MeVTdec(ν ,μ τ) ~ 3 MeV

T~MeVt~sec

Free-streaming neutrinos

(decoupled)Cosmic Neutrino

Background

Neutrinos coupled by weak

interactions(in equilibrium)

Neutrinos keep the energy spectrum of a relativistic

fermion with eq form

1e1

T)(p,f p/T +=ν

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos

γγ→+ -ee

Neutrino and Photon (CMB) temperatures

1e1

T)(p,f p/T +=

νν

1/3

411

T

T

=

ν

γ

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos

γγ→+ -ee

Neutrino and Photon (CMB) temperatures

1e1

T)(p,f p/T +=

νν

1/3

411

T

T

=

ν

γ

Photon temp falls

slower than 1/a(t)

• Number density

• Energy density

323

3

113(6

113

2 CMBγννν Tπ

)ζn)(p,Tf

π)(pd

n === ∫

→+= ∫νν

νν

π

ρnm

T

)(p,Tfπ)(pd

mp

i

ii

CMB

νν

43/42

3

322

114

1207

2

Massless

Massive mν>>T

Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species 1e

1T)(p,f p/T +

=νν

The Cosmic Neutrino Background

The Cosmic Neutrino Background

• Number density

• Energy density

323

3

113(6

113

2 CMBγννν Tπ

)ζn)(p,Tf

π)(pd

n === ∫

→+= ∫νν

νν

π

ρnm

T

)(p,Tfπ)(pd

mp

i

ii

CMB

νν

43/42

3

322

114

1207

2

Massless

Massive

mν>>T

Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species 1e

1T)(p,f p/T +

=νν

At present 112 per flavour cm )( -3νν +

Contribution to the energy density of the Universe

eV 94.1

mh Ω i

i2

∑=ν

52 101.7h Ω −×=ν

At T<me, the radiation content of the Universe is

Relativistic particles in the Universe

γνγνγ ρππρρρ

+=××+=+= 3114

87

1158

73

15

3/44

24

2

r TT

At T<me, the radiation content of the Universe is

Effective number of relativistic neutrino speciesTraditional parametrization of the energy densitystored in relativistic particles

Relativistic particles in the Universe

data) (LEP 008.0984.2 ±=νN# of flavour neutrinos:

• Extra radiation can be:

scalars, pseudoscalars, sterile neutrinos (totally or partially thermalized, bulk), neutrinos in very low-energy reheating scenarios, relativistic decay products of heavy particles…

• Particular case: relic neutrino asymmetries

Constraints from BBN and from CMB+LSS

Extra relativistic particles

At T<me, the radiation content of the Universe is

Effective number of relativistic neutrino speciesTraditional parametrization of the energy densitystored in relativistic particles

Neff is not exactly 3 for standard neutrinos

Relativistic particles in the Universe

data) (LEP 008.0984.2 ±=νN# of flavour neutrinos:

But, since Tdec(ν) is close to me, neutrinos share a small part of the entropy release

At T~me, e+e- pairs annihilate heating photonsγγ→+ -ee

Non-instantaneous neutrino decoupling

fν=fFD(p,Tν)[1+ f(p)]δ

Momentum-dependent Boltzmann equation

9-dim Phase Space ProcessΣPi conservation

Statistical Factor

),(),( 111

tpItpfdpd

Hpdtd

coll=

− ν

+ evolution of total energy density:

ν e

ν µ ,τ

f x10δ

1e

pp/T

2

+

δ ρ ν e(

%)

δ ρ ν µ

(%)

δ ρ ν τ(

%)Neff

Instantaneous decoupling

1.40102

0 0 0 3

SM+3ν mixing(θ13=0)

1.3978 0.73 0.52 0.52 3.046

γγ0/TTfin

Mangano et al, NPB 729 (2005) 221

Non-instantaneous neutrino decoupling

Dolgov, Hansen & Semikoz, NPB 503 (1997) 426Mangano et al, PLB 534 (2002) 8

Changes in CNB quantities

• Contribution of neutrinos to total energy density today (3 degenerate masses)

• Present neutrino number density€

Ων=ρν

ρc

= 3m0

94.12h2 eV2 2eV 20

14.933hm=νΩ

€

nν=335.7 cm­3

€

nν=339.3 cm­3

Neff varying the neutrino decoupling temperature

End of 1st lecture

Exercises: try to calculate…

• The present number density of massive/massless neutrinos nν

0 in cm-3

• The present energy density of massive/massless neutrinos Ων

0 and find the limits on the total neutrino mass from Ων

0<1 and Ων0 <Ωm

0

• The final ratio Tγ /Tν using the conservation of entropy density before/after e± annihilations

• The decoupling temperature of relic neutrinos using Γ≈ Η

• The evolution of Ω(ν,γ ,b,cdm) with the expansion for (3,0,0), (1,1,1) and (0.05,0.009,0) [masses in eV]

• The value of Neff if neutrinos decouple at Tdec in [5,0.2] MeV