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### 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

Neutrino Background

Relic neutrino decoupling

New results in the SM

and in presence of

electron-neutrino NSI

OutlinePrecise calculation

of the relic neutrino

density

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

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

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 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

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos

Precise calculation of neutrino decoupling:

SM + flavour oscillations

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) temperatures

At T~me, electron-positron pairs annihilate

heating photons but not the decoupled neutrinos

+ evolution of total energy density:

Momentum-dependent Boltzmann equationStatistical 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

Evolution of fν for a particular momentum p=10T

Relativistic particles in the Universe

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

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 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

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

Mangano et al, NPB 729 (2005) 221

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

Present neutrino number density

Changes in CNB quantitiesPrecise calculation of neutrino decoupling:

Non-standard neutrino-electron interactions

Limits on from scattering experiments,

LEP data, solar vs Kamland data…

Electron-Neutrino NSIBreaking 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 Tdec in presence of NSI

SM

SM

Contours of equal Tdec in MeV with diagonal NSI parameters

Effects of NSI on the neutrino spectral distortions

Here larger

variation for ,

Neutrinos keep thermal contact

with e- until smaller temperatures

Departure from Neff=3 not observable from present cosmological data

Mangano et al, hep-ph/0612150

…but maybe in the near future ?

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

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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