Cosmological Aspects of Neutrino Physics (I)

04/22/23

Cosmological Aspects of Neutrino Physics (I)

Sergio Pastor (IFIC)61st SUSSP

St Andrews, August 2006

ν

Cosmological Aspects of Neutrino Physics1st 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~

eV

Neutrino 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

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Relic neutrinos influence several cosmological epochs

T < eVT ~ MeV

Formation of Large Scale Structures

LSS

Cosmic Microwave Background

CMB

Primordial

Nucleosynthesis

BBN

No flavour sensitivity Neff & mννevs νμ,τ Neff

Basics of cosmology: background evolution

1st lecture

Introduction: neutrinos and the History of the Universe

Relic neutrino production and decoupling

Cosmological Aspects of Neutrino Physics

Neutrinos and Primordial Nucleosynthesis

Neutrino oscillations in the Early Universe*

* Advanced topic

Cosmological Aspects of Neutrino Physics

2nd & 3rd lectures

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

* Advanced topic

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. Hannestadhep-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

1θdφrdθr

kr

dra(t)dtdxdxgds νμ

μν

gGTRgRG 82

1

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

pguupT )(

Eqs in the SM of Cosmology

)(3.

ppHdt

d

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

3

8)(

a

kG

a

atH

00 component

(Friedmann eq)

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

1)( 22

atH

k

ρcrit=3H2/8πG is the critical density

Ω= ρ/ρcrit

Evolution of the Universe

)3(3

4..

pG

a

a

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

a

a

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

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Evolution of the background densities: 1 MeV → now

3 neutrino species

with different masses

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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


interactions(in equilibrium)

1e1

T)(p,f p/T

-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 M

πρT G

M

πρ n , HσΓ ν

decp

RF

p

Rww 1

3

8

3

8v

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(νμ,τ) ~ 3 MeV

T~MeVt~sec

Free-streaming neutrinos

(decoupled)Cosmic Neutrino

Background


interactions(in equilibrium)

Neutrinos keep the energy spectrum of a relativistic

fermion with eq form

1e1

T)(p,fp/T

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos

γγ -ee

Neutrino and Photon (CMB) temperatures

1e1

T)(p,fp/T

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,fp/T

1/3

411

T

T

ν

γ

Photon temp falls

slower than 1/a(t)

• Number density

• Energy density

323

3

11

3(6

11

3

2 CMBγννν Tπ

)ζn)(p,Tf

π)(

pdn

nm

T

)(p,Tfπ)(

pdmp

i

ii

CMB

νν

43/42

3

322

11

4

120

7

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

The Cosmic Neutrino Background

The Cosmic Neutrino Background

• Number density

• Energy density

323

3

11

3(6

11

3

2 CMBγννν Tπ

)ζn)(p,Tf

π)(

pdn

nm

T

)(p,Tfπ)(

pdmp

i

ii

CMB

νν

43/42

3

322

11

4

120

7

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

At present 112 per flavour cm )( -3

Contribution to the energy density of the Universe

eV 93.2

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

311

4

8

71

158

73

15

3/44

24

2

r TT


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


data) (LEP 008.0984.2 N# 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


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

Neff is not exactly 3 for standard neutrinos


data) (LEP 008.0984.2 N# 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

f=fFD(p,T)[1+δf(p)]

Boltzmann Equation

9-dim Phase Space ProcessPi conservation

Statistical Factor

e

,

δf x10

1e

pp/T

2

ρ(e) 0.73% largerρ() 0.52% larger

fν=fFD(p,Tν)[1+δf(p)]

Mangano et al 2002

Non-instantaneous neutrino decoupling

Non-instantaneous decoupling + QED corrections to e.m. plasma+ Flavor Oscillations

Neff=3.046 T.Pinto et al, NPB 729 (2005) 221

40102.14

113/1

T

T

3978.1)( taT

Produced elements: D, 3He, 4He, 7Li and

small abundances of others

BBN: Creation of light

elements

Theoretical inputs:

Range of temperatures: from 0.8 to 0.01 MeV

BBN: Creation of light elements

n/p freezing and neutron decay

Phase I: 0.8-0.1 MeVn-p reactions

BBN: Creation of light elements

0.03 MeV

0.07 MeV

Phase II: 0.1-0.01 MeVFormation of light nuclei starting from D

Photodesintegrationprevents earlier formation for temperatures closer to nuclear binding energies

BBN: Measurement of Primordial abundances

Difficult task: search in astrophysical systems with chemical evolution as small as possible

Deuterium: destroyed in stars. Any observed abundance of D is a lower limit to the primordial abundance. 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 analysis

Helium-4: primordial abundance increased by H burning in stars. Data from low metallicity, extragalatic HII regions

Lithium-7: destroyed in stars, produced in cosmic ray reactions.Data from oldest, most metal-poor stars in the Galaxy

Fields & Sarkar PDG 2004

BBN: Predictions vs Observations

after WMAPΩBh2=0.023±0.001

Effect of neutrinos on BBN 1. Neff fixes the expansion rate during BBN

(Neff)>0 4He

Burles, Nollett & Turner 1999

2p3M

8π H

3.4 3.2

3.0

2. Direct effect of electron neutrinos and antineutrinos on the n-p reactions

BBN: allowed ranges for Neff

Cuoco et al, IJMP A19 (2004) 4431 [astro-ph/0307203]

Using 4He + D data (2σ)

1.10.9eff 2.5N

Neutrino oscillations in the Early Universe

Neutrino oscillations are effective when medium effects get small enough

Compare oscillation term with effective potentials

Strumia & Vissani, hep-ph/0606054

Oscillation term prop. to Δm2/2E

First order matter effects prop. toGF[n(e-)-n(e+)]

Second order matter effects prop. to

GF(E/MZ)2[n(e-)+n(e+)]

Coupled neutrinos

Flavor neutrino oscillations in the Early Universe

Standard case: all neutrino flavours equally populated oscillations are effective below a few MeV, but have

no effect (except for mixing the small distortions δfν)Cosmology is insensitive to neutrino flavour after decoupling!

Non-zero neutrino asymmetries: flavour oscillations lead

to (almost) equilibrium for all μν

What if additional, sterile neutrino species are mixed with the flavour neutrinos?

If oscillations are effective before decoupling: the additional species can be brought into equilibrium: Neff=4

If oscillations are effective after decoupling: Neff=3 but the spectrum of active neutrinos is distorted (direct effect of νe and anti-νe on BBN)

Active-sterile neutrino oscillations

Results depend on the sign of Δm2

(resonant vs non-resonant case)


Dolgov & Villante, NPB 679 (2004) 261

Additional neutrino

fully in eq

Flavour neutrino spectrum depleted



Additional neutrino

fully in eq


Kirilova, astro-ph/0312569



Additional neutrino

fully in eq


End of 1st lecture

Cosmological Aspects of Neutrino Physics (I)

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