Precise calculation of the relic neutrino density

Sergio Pastor (IFIC)

ν

JIGSAW 2007TIFR Mumbai, February 2007

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

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

Outline

Precise calculation of the relic neutrino density

New results in the SM and in presence of

electron-neutrino NSI

Introduction: the Cosmic Neutrino Background

Relic neutrino decoupling

The CNB

T~MeVt~sec

Neutrinos coupled by weak

interactions(in equilibrium)

1e1

T)(p,f p/Tν

Primordial

Nucleosynthesis

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/Tν

Primordial

Nucleosynthesis

• 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

Relic neutrino decoupling

-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 1T νdec

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

Neutrinos coupled by weak

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

Precise calculation of neutrino decoupling:

SM + flavour oscillations

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)]

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

Momentum-dependent Boltzmann equation

9-dim Phase Space ProcessPi conservation

Statistical Factor

),(),( 111

tpItpfdp

dHp

dt

dcoll

+ evolution of total energy density:

For T>2 MeV neutrinos are coupled

Between 2>T/MeV>0.1distortions grow

At lower temperaturesdistortions freeze out

f e f

Evolution of fν for a particular momentum p=10T

Evolution of fν for a particular momentum p=10T

Final spectral distortion

e

,

δf x10

1e

pp/T

2

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

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 N# of flavour neutrinos:

Bounds from BBN and from CMB+LSS

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 N# of flavour neutrinos:

e(%) (%) (%) Neff

Instantaneous decoupling

1.40102 0 0 0 3

SM 1.3978 0.94 0.43 0.43 3.046

0/TT fin

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

Results

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

GFE/MZ2[ρ(e-)+ρ(e+)]

Coupled neutrinos

Previous work by Hannestad,PRD 65 (2002) 083006

Around T~1 MeV the oscillationsstart to modifythe distortion

The variationis larger for e

Effects of flavour neutrino oscillations on the spectral distortions

Around T~1 MeV the oscillationsstart to modifythe distortion

The variationis larger for e

The differencebetween differentflavors is reduced

Effects of flavour neutrino oscillations on the spectral distortions

Oscillations smooth the flavour dependence of the distortion

e(%) (%) (%) Neff

Instantaneous decoupling

1.40102 0 0 0 3

SM 1.3978 0.94 0.43 0.43 3.046

+3ν mixing(θ13=0) 1.3978 0.73 0.52 0.52 3.046

+3ν mixing(sin2θ13=0.047)

1.3978 0.70 0.56 0.52 3.046

0/TT fin

Mangano et al, NPB 729 (2005) 221

Results

Changes in CNB quantities

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

• Present neutrino number density

c

3m0

94.12h2 eV2 2eV 20

14.93

3

h

m

n 335.7 cm-3

n 339.3 cm-3

Precise calculation of neutrino decoupling:

Non-standard neutrino-electron interactions

Electron-Neutrino NSI

New effective interactions between electron and neutrinos

Electron-Neutrino NSI

Breaking of Lepton universality (=) Flavour-changing (≠ )

Limits on from scattering experiments, LEP data, solar vs Kamland data…

RL,

Berezhiani & Rossi, PLB 535 (2002) 207Davidson et al, JHEP 03 (2003) 011Barranco et al, PRD 73 (2006) 113001

Analytical calculation of Tdec in presence of NSIAnalytical calculation of Tdec in presence of NSI

Contours of equal Tdec in MeV with diagonal NSI parameters

SM SM

Neff varying the neutrino decoupling temperatureNeff varying the neutrino decoupling temperature

Effects of NSI on the neutrino spectral distortions

Here largervariation for ,

Neutrinos keep thermal contact with e- until smaller temperatures

e(%) (%) (%) Neff

Instantaneous decoupling

1.40102 0 0 0 3

+3ν mixing(θ13=0) 1.3978 0.73 0.52 0.52 3.046

Lee= 4.0 Ree= 4.0

1.3812 9.47 3.83 3.83 3.357

0/TT fin

Mangano et al, NPB 756 (2006) 100

Results

Very large NSI parameters, FAR from allowed regions

e(%) (%) (%) Neff

Instantaneous decoupling

1.40102 0 0 0 3

+3ν mixing(θ13=0) 1.3978 0.73 0.52 0.52 3.046

Lee= 0.12 Ree= -1.58L= -0.5 R= 0.5

Le= -0.85 Re= 0.38

1.3937 2.21 1.66 0.52 3.120

0/TT fin

Mangano et al, NPB 756 (2006) 100

Results

Large NSI parameters, still allowed by present lab data

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

Bowen et al MNRAS 2002

ΔNeff ~ 3 (WMAP)

ΔNeff ~ 0.2 (Planck)

Bashinsky & Seljak PRD 69 (2004) 083002Example of futureCMB satellite

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)

Conclusions

ν

Cosmological observables can be used to bound (or measure) neutrino properties,

once the relic neutrino spectrum is known