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Cosmological Aspects of Neutrino Physics (I). ν. Sergio Pastor (IFIC) 61st SUSSP St Andrews, August 2006. Cosmological Aspects of Neutrino Physics. 1st lecture. Introduction: neutrinos and the History of the Universe. This is a neutrino!. Neutrinos coupled by weak interactions.

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Cosmological aspects of neutrino physics i

Cosmological Aspects of Neutrino Physics (I)

ν

Sergio Pastor (IFIC)

61st SUSSP

St Andrews, August 2006


Cosmological aspects of neutrino physics
Cosmological Aspects of Neutrino Physics

1st lecture

Introduction: neutrinos and the History of the Universe


This is a

neutrino!


Neutrinos coupled by weak interactions
Neutrinos coupled by weak interactions

Decoupled neutrinos

(Cosmic Neutrino Background or CNB)

Primordial

Nucleosynthesis

T~MeV

t~sec


Relativistic neutrinos
Relativistic neutrinos

At least 1 species is NR

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


Primordial

Nucleosynthesis

BBN

Cosmic Microwave Background

CMB

Formation of Large Scale Structures

LSS

T ~ MeV

T < eV

νevsνμ,τ Neff

No flavour sensitivityNeff & mν

Relic neutrinos influence several cosmological epochs


Cosmological aspects of neutrino physics1
Cosmological Aspects of Neutrino Physics

1st lecture

Introduction: neutrinos and the History of the Universe

Basics of cosmology: background evolution

Relic neutrino production and decoupling

Neutrinos and Primordial Nucleosynthesis

Neutrino oscillations in the Early Universe*

* Advanced topic


Cosmological aspects of neutrino physics2
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 Nνfrom cosmology

* Advanced topic


Suggested References

Books

Modern 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 reviews

Neutrino 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. Hannestad

hep-ph/0602058

BBN and Physics beyond the Standard Model, S. Sarkar

Rep. Prog. Phys. 59 (1996) 1493-1610 [hep-ph/9602260]


Eqs in the sm of cosmology
Eqs in the SM of Cosmology

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


Eqs in the sm of cosmology1

00 component (Friedmann eq)

ρ=ρM+ρR+ρΛ

H(t) is the Hubble parameter

Eq of state p=αρ

ρ = const a-3(1+α)

Radiation α=1/3 Matter α=0 Cosmological constantα=-1

ρR~1/a4ρM~1/a3ρΛ~const

Eqs in the SM of Cosmology

Ω= ρ/ρcrit

ρcrit=3H2/8πG is the critical density


Evolution of the universe

accélération

acceleration

décélération lente

slow deceleration

décélération rqpide

fast deceleration

accélération

acceleration

accélération

?

décélération lente

décélération rqpide

accélération

inflation

RD (radiation domination)

MD (matter domination)

dark energy domination

inflation

radiation

matière

énergie noire

Evolution of the Universe

a(t)~eHt

a(t)~t1/2

a(t)~t2/3


Evolution of the background densities: 1 MeV → now

3 neutrino species with different masses


photons

neutrinos

Λ

cdm

m3=0.05 eV

baryons

m2=0.009 eV

m1≈ 0 eV

Evolution of the background densities: 1 MeV → now

Ωi= ρi/ρcrit


Equilibrium thermodynamics

Distribution function of particle momenta in equilibrium

Thermodynamical variables

Equilibrium thermodynamics

Particles in equilibrium

when T are high and

interactions effective

T~1/a(t)


Neutrinos coupled by weak interactions in equilibrium
Neutrinos coupled by weak interactions(in equilibrium)

Primordial

Nucleosynthesis

T~MeV

t~sec


Neutrinos in equilibrium
Neutrinos in Equilibrium

1 MeV  T mμ

Tν= Te = Tγ


Neutrino decoupling
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

Rough, but quite accurate estimate of the decoupling temperature

Rate of weak processes ~ Hubble expansion rate

Since νe have both CC and NC interactions withe±

Tdec(νe) ~ 2 MeV

Tdec(νμ,τ) ~ 3 MeV


Neutrinos coupled by weak interactions in equilibrium1
Neutrinos coupled by weak interactions(in equilibrium)

Free-streaming neutrinos (decoupled)

Cosmic Neutrino Background

Neutrinos keep the energy

spectrum of a relativistic

fermion with eq form

T~MeV

t~sec


Neutrino and photon cmb temperatures
Neutrino and Photon (CMB) temperatures

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos


Neutrino and photon cmb temperatures1
Neutrino and Photon (CMB) temperatures

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos

Photon temp falls

slower than 1/a(t)


The cosmic neutrino background

Neutrinos decoupled at T~MeV, keeping a

spectrum as that of a relativistic species

The Cosmic Neutrino Background

  • Number density

  • Energy density

Massless

Massive mν>>T


The cosmic neutrino background1

Neutrinos decoupled at T~MeV, keeping a

spectrum as that of a relativistic species

Contribution to the energy

density of the Universe

At present 112 per flavour

The Cosmic Neutrino Background

  • Number density

  • Energy density

Massless

Massive

mν>>T


Relativistic particles in the universe
Relativistic particles in the Universe

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


Relativistic particles in the universe1

# of flavour neutrinos:

Relativistic particles in the Universe

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

Effective number of relativistic neutrino species

Traditional parametrization of the energy density

stored in relativistic particles


Extra relativistic particles
Extra relativistic particles

  • 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


Relativistic particles in the universe2

# of flavour neutrinos:

Relativistic particles in the Universe

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

Effective number of relativistic neutrino species

Traditional parametrization of the energy density

stored in relativistic particles

Neff is not exactly 3 for standard neutrinos


Non instantaneous neutrino decoupling
Non-instantaneous neutrino decoupling

At T~me, e+e- pairs annihilate heating photons

But, since Tdec(ν) is close to me, neutrinos

share a small part of the entropy release

f=fFD(p,T)[1+δf(p)]


Boltzmann equation
Boltzmann Equation

Statistical Factor

9-dim Phase Space

Pi conservation

Process


δf x10

e

,


Non instantaneous neutrino decoupling1
Non-instantaneous neutrino decoupling

fν=fFD(p,Tν)[1+δf(p)]

ρ(e) 0.73% larger

ρ(,) 0.52% larger

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

+ Flavor Oscillations

Neff=3.046

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

Mangano et al 2002


Bbn creation of light elements

Theoretical inputs:

BBN: Creation of light elements

Produced elements: D, 3He, 4He, 7Li and small abundances of others


Bbn creation of light elements1
BBN: Creation of light elements

Range of temperatures: from 0.8 to 0.01 MeV

Phase I: 0.8-0.1 MeV

n-p reactions

n/p freezing and neutron decay


Bbn creation of light elements2
BBN: Creation of light elements

Phase II: 0.1-0.01 MeV

Formation of light nuclei starting from D

Photodesintegration

prevents earlier formation for temperatures closer

to nuclear binding energies

0.07 MeV

0.03 MeV


Bbn creation of light elements3
BBN: Creation of light elements

Phase II: 0.1-0.01 MeV

Formation of light nuclei starting from D

Photodesintegration

prevents earlier formation for temperatures closer

to nuclear binding energies

0.07 MeV

0.03 MeV


Bbn measurement of primordial abundances
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


Bbn predictions vs observations
BBN: Predictions vs Observations

after WMAP

ΩBh2=0.023±0.001

Fields & Sarkar PDG 2004


Effect of neutrinos on bbn

1. Neff fixes the expansion rate during BBN

3.4

3.2

3.0

(Neff)>0 4He

Burles, Nollett & Turner 1999

Effect of neutrinos on BBN

2. Direct effect of electron neutrinos and antineutrinos

on the n-p reactions


Bbn allowed ranges for n eff
BBN: allowed ranges for Neff

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

Using 4He + D data (2σ)


Neutrino oscillations in the early universe
Neutrino oscillations in the Early Universe

Neutrino oscillations are effective when medium effects get small enough

Compare oscillation term with effective potentials

Coupled neutrinos

Oscillation term prop.

to Δm2/2E

Second order matter

effects prop. to

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

First order matter

effects prop. to

GF[n(e-)-n(e+)]

Strumia & Vissani, hep-ph/0606054


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!

Flavor neutrino oscillations in the Early Universe

Non-zero neutrino asymmetries: flavour oscillations lead

to (almost) equilibrium for all μν


Active sterile neutrino oscillations
Active-sterile neutrino oscillations

  • 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=3but the spectrum of active neutrinos is distorted(direct effect of νe and anti-νe on BBN)

Results depend on the sign of Δm2

(resonant vs non-resonant case)


Active sterile neutrino oscillations1
Active-sterile neutrino oscillations

Additional neutrino fully in eq

Flavour neutrino spectrum depleted

Dolgov & Villante,

NPB 679 (2004) 261


Active sterile neutrino oscillations2

Kirilova, astro-ph/0312569

Active-sterile neutrino oscillations

Additional neutrino fully in eq

Flavour neutrino spectrum depleted

Dolgov & Villante,

NPB 679 (2004) 261


Active sterile neutrino oscillations3
Active-sterile neutrino oscillations

Additional neutrino fully in eq

Flavour neutrino spectrum depleted

Dolgov & Villante,

NPB 679 (2004) 261


Active sterile neutrino oscillations4
Active-sterile neutrino oscillations

Additional neutrino fully in eq

Dolgov & Villante,

NPB 679 (2004) 261



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