Does WMAP data constrain the Does WMAP data constrain the lepton asymmetry of the Universe to lepton asymmetry of the Universe to

be zero?be zero?M. LattanziM. Lattanzi*, R*, R. Ruffini, G.V. Vereshchagin. Ruffini, G.V. Vereshchagin

Dip. di Fisica - Università di Roma “La Sapienza” ICRA – International Center for Relativistic Astrophysics

Albert Einstein Century International Conference

Paris, 18 – 22 July 2005

* ML participation to this meeting has been supported by the Royal Astronomical Society

The advent of the so-called “Precision Cosmology” has allowed to measure the values of the cosmological parameters with ever-increasing accuracy.

(Spergel et al., 2003)

The cosmological observables are sensitive to neutrino properties and can then be used to determine them.

For example, the relation:

eV5.92

2 mh

together with . 1, yields (using h = 0.7):

(Gerstein & Zel’dovich, 1966)

eV45

m

• Thermal equilibrium between e§,

• Perfect lepton symmetry

• No mechanisms for entropy generation other than e+e-

annihilation

• Stable neutrinos

• No interactions that diminishes the number of neutrinos

• Absence of right-handed neutrinos

• 3 neutrino species, (nearly) degenerate in mass

Only one unknown quantity: m

In the standard cosmological scenario, the following assumptions about neutrinos are made:

The Standard Scenario

The cosmological observables are sensitive to neutrino properties and can then be used to determine them.

WMAP + 2dFGRS + Ly-a Forest

mi < 0.7 eV

(Spergel et al., 2003)

From tritium -decay:

me < 2.8 eV(Bonn et al., 2002)

From 0:

|mee | < 0.5 eV(Klapdor-Kleingrothaus, 2001)

Spergel et al., 2003 WMAPex+2dF+Ly m0.7 eV 95% CL

Hannestad, 2003 WMAP+2dF m1 eV 95% CL

Allen, Schmidt & Bridle, 2003

WMAPex+2dF+XLF m0.56 § 0.26 eV 68% CL

Barger, Marfatia & Tregre, 2004

WMAPex+2dF+SDSS+HST

m0.74 eV 95% CL

Tegmark et al., 2004 WMAP+SDSS m1.7 eV 95% CL

Hannestad & Raffelt, 2004

WMAP+2dF+SDSS+HST+SNIa

m0.34 eV (std)

m1.0 eV (3+1)95% CL

Crotty & Lesgourgues, 2004

WMAP+ACBAR+2dF+SDSS+HST+SNIa

m0.6 ¥ 1.5 eV 95% CL

Summary of cosmological bounds on m

However, the total mass is just part of the story.

Each one of the above assumptions could be not valid in presence of physics beyond the Standard Model of particle physics, including (but not limited to) :

• Existence of Majorons

• Annihilation of supersymmetric particles

• Existence of sterile neutrinos

• Non-standard leptogenesis (es. Affleck-Dine scenarios)

• Existence of right handed neutrinos

To what extent cosmological observables can constraint these non-standard scenarios?

Non-Standard Scenarios

Thermal Evolution

Supposing a thermal spectrum, the neutrinos follow a Fermi-Dirac distribution:

= dTd

From this we can compute the energy density and the number density:

In the standard scenario:

for each species. It is then customary to

define:

Parameterization of Non-Standard Scenarios

In principle, the following parameters are needed in order to fully describe the neutrino sector in a non-standard scenario:

• The number N of neutrino species;

• N values of mass mi;

• N values of degeneracy parameter i;

• N values of temperature Ti;

• The total effective number of relativistic species Neff

However, in practice every cosm. obs. is sensitive only to some of (or to some combination of) the above parameters

Lepton Asymmetry

At the present, there are no observational evidence that the L.A. of the Universe is small (i.e., comparable to the baryon asymmetry).

Several well-motivated particle physics scenario producing a large lepton asymmetry exists.

Testing the prediction of such scenarios would be very important, since it could shed light on leptogenesis and baryogenesis, and give information on the elements of the neutrino mixing matrix.

The presence of a lepton asymmetry involves a non zero neutrino degeneracy parameter (i.e., dimensionless chemical potential).

However this is not enough, since standard BBN and neutrino oscillation strongly disfavour a non-zero degeneracy parameter.

Some other species is required in order to avoid equalization.

Minimum number of extra parameters is two: and Neff

The presence of changes shape of the distribution function of neutrinos.

Three main effects:

• Larger number density at the presen time:

• Larger energy density:

• Different velocity distribution (larger mean speed and more populated tail of particles with “large” momentum).

)(eV5.92 2

2

J

mh

Important for Landau damping

Effects of Lepton Asymmetry

Distribution of momenta for

=0, 1, 3

T

py

• Different velocity distribution (larger mean speed and more populated tail of particles with “large” momentum).

•Different velocity distribution (larger mean speed and more populated tail of particles with “large” momentum).

Time evolution of the mean squared speed for =0 and m=0.1, 1 eV.

•Different velocity distribution (larger mean speed and more populated tail of particles with “large” momentum).

Time evolution of the “sound speed” normalize to the case =0, per =1, 2, 3

We consider a flat CDM model described by the usual parameters (b, m, h, n, , A).

We parameterize the neutrino sector with 3 parameters:

• The density parameter of neutrinos ´h2;

• A common degeneracy parameter

• The extra energy density in UR species other than neutrinos:

where

Likelihood analysis(ML, Ruffini &

Vereshchagin, submitted to PRD)

We consider the following region in parameter space

• 0.020 · b · 0.028

• 0.10 · m · 0.18

• 0.90 · n · 1.10

• 0 · · 0.30

• 0.70 · A · 1.10

• 0 · · 0.03

• 0 · · 2.0

• 0 · Neffoth · 2.0

We sample the likelihood function with respect to the TT and TE WMAP spectra on a grid of 5 equispaced points in every direction

We use a modified version of the code CMBFast to compute the

theoretical spectra

Assunzioni:• = 1• h = 0.72• N = 3

Parameter Space

Neutrino mass:

• 0 is preferred value• @95% confidence level,

m < 1.2 eV This is quite in agreementwith previous analyses(somewhat looser, probablydue to too large spacingin thegrid)

Number of extra relativisticspecies :

• 0.70 is preferred value• @95% confidence level,

-0.5 < Neff < 2 This is also quite in agreement with previous analyses(see eg Crotty, Lesgourguesand Pastor 2003 and 2004)

Degeneracy Parameter andLepton Asymmetry:

• || = 0.70 (|L|=0.46)is the preferred value

• @95% confidence level,0 < || < 1.10 < |L| < 0.8

We have also computed the 95% confidence region for , for different values the number of extra relativistic species

The smaller is Neffoth, the largest is the best-fit value of the

degeneracy parameter.For low values, zero deg. par. is outside the 95% CL.

Correlation between and Neffoth

Neffoth

0 0.65 § 0.58

0.5 0.42+0.58-0.42

1.0 0.18+0.58-0.18

1.5 < 0.53

2.0 < 0.29

Summary• In the standard cosmological scenario, the only unknown parameter related to relic neutrinos is the sum of masses (considered nearly degenerate).

• However, non-standard models are motivated by extensions of the standard model of particle physics.

• One possible modification is the introduction of a cosmological lepton asymmetry.

• Although WMAP data are well-fitted by asymmetric models, nevertheless they seem not to rule out a lepton-symmetric Universe.

• This is probably due to the fact that CMB measurements cannot disentangle lepton asym. from other sources of extra energy density.

• The linear part of the matter power spectrum could help for this.

• Anyway, preference for non-zero N is an hint for the presence of physics beyon SM.