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ν. Precise calculation of the relic neutrino density. Sergio Pastor (IFIC). In collaboration with T. Pinto, G, Mangano, G. Miele, O. Pisanti and P.D. Serpico NPB 729 (2005) 221 , NPB 756 (2006) 100. JIGSAW 2007 TIFR Mumbai, February 2007. Introduction: the Cosmic Neutrino Background.

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Precise calculation of the relic neutrino density

ν

Precise calculation of the relic neutrino density

Sergio Pastor (IFIC)

In collaboration with T. Pinto, G, Mangano, G. Miele, O. Pisanti and P.D. Serpico

NPB 729 (2005) 221 , NPB 756 (2006) 100

JIGSAW 2007

TIFR Mumbai, February 2007


Outline

Introduction: the Cosmic

Neutrino Background

Relic neutrino decoupling

New results in the SM

and in presence of

electron-neutrino NSI

Outline

Precise calculation

of the relic neutrino

density



Neutrinos coupled by weak interactions(in equilibrium)

T~MeV

t~sec

Primordial

Nucleosynthesis


Neutrinos coupled by weak interactions in equilibrium
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

Primordial

Nucleosynthesis

T~MeV

t~sec


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



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



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)]


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

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos


Momentum dependent boltzmann equation

+ evolution of total energy density:

Momentum-dependent Boltzmann equation

Statistical Factor

9-dim Phase Space

Pi conservation

Process


Evolution of fν for a particular momentum p=10T

At lower

temperatures

distortions

freeze out

Between 2>T/MeV>0.1

distortions grow

For T>2 MeV neutrinos are coupled


Final spectral distortion

Evolution of fν for a particular momentum p=10T


δf x10

e

,


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

Bounds 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


Results

Dolgov, Hansen & Semikoz, NPB 503 (1997) 426

Mangano et al, PLB 534 (2002) 8


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

GFE/MZ2[ρ(e-)+ρ(e+)]

First order matter

effects prop. to

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

Strumia & Vissani, hep-ph/0606054

Previous work by Hannestad,

PRD 65 (2002) 083006


Effects of flavour neutrino oscillations on the spectral distortions

The variation

is larger for e

Around

T~1 MeV

the oscillations

start to modify

the distortion


Effects of flavour neutrino oscillations on the spectral distortions

The variation

is larger for e

Around

T~1 MeV

the oscillations

start to modify

the distortion

The difference

between different

flavors is reduced

Oscillations smooth the flavour

dependence of the distortion


Results distortions

Mangano et al, NPB 729 (2005) 221


Changes in cnb quantities

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

Present neutrino number density

Changes in CNB quantities


Precise calculation of neutrino decoupling: degenerate masses)

Non-standard neutrino-electron interactions


Electron neutrino nsi

New degenerate masses)effective interactions between electron and neutrinos

Electron-Neutrino NSI


Electron neutrino nsi1

Limits on from scattering experiments, degenerate masses)

LEP data, solar vs Kamland data…

Electron-Neutrino NSI

Breaking of Lepton universality (=)

Flavour-changing (≠ )

Berezhiani & Rossi, PLB 535 (2002) 207

Davidson et al, JHEP 03 (2003) 011

Barranco et al, PRD 73 (2006) 113001


Analytical calculation of T degenerate masses)dec in presence of NSI

SM

SM

Contours of equal Tdec in MeV with diagonal NSI parameters



Effects of NSI on the neutrino spectral distortions degenerate masses)

Here larger

variation for ,

Neutrinos keep thermal contact

with e- until smaller temperatures


Results degenerate masses)

Very large NSI parameters,

FAR from allowed regions

Mangano et al, NPB 756 (2006) 100


Results degenerate masses)

Large NSI parameters, still

allowed by present lab data

Mangano et al, NPB 756 (2006) 100


Departure from n eff 3 not observable from present cosmological data
Departure from N degenerate masses)eff=3 not observable from present cosmological data

Mangano et al, hep-ph/0612150


But maybe in the near future
…but maybe in the near future ? degenerate masses)

Forecast analysis:

CMB data

ΔNeff ~ 3 (WMAP)

ΔNeff ~ 0.2 (Planck)

Bowen et al MNRAS 2002

Example of future

CMB satellite

Bashinsky & Seljak PRD 69 (2004) 083002


Conclusions
Conclusions degenerate masses)

Cosmological observables can be used to

bound (or measure) neutrino properties, once the relic neutrino spectrum is known

ν

The small spectral distortions from relic neutrino—electron processes can be

precisely calculated, leading to Neff=3.046

(or up to 3 times more including NSI)


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