G. Mangano 1 Relic Neutrino Distribution Gianpiero Mangano INFN, Sezione di Napoli Italy

G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia 11

Relic Neutrino DistributionRelic Neutrino Distribution

Gianpiero ManganoGianpiero ManganoINFN, Sezione di NapoliINFN, Sezione di Napoli

ItalyItaly

22G. ManganoG. Mangano NOVE2006@VeneziaNOVE2006@Venezia


Pseudo-thermal distribution: T = 1.95 K

Number density ( v + v ): 112 cm-3 /flavor

Mean kinetic energy: 10-7(eV/m) eV

Direct searches:

GF2me Ev 10-50 (Ev/eV) cm2 hopeless ?

Standard picture

Indirect searches: cosmological observables

neutrino influence weak + gravity (T> 1 MeV)

gravity (T< 1 MeV)


How strong are present (and future) bounds

on exotic features in v distribution?

General parametrization

nnanxa xPa

exxf )(

1)(

2

Pn orthogonal polynomials with respect to Fermi-Dirac distribution

an in one to one correspondence with moments of distribution Qn

dxxxfQ nn 2)(41

3

2

3002

411

7120

411058.0

TQN

TQeVmh

eff

v


),())(/exp(

),,,,(),( )( tktTmktmBP

etkf tt

122

unstable v’s: tot, LSS, CMB, e+ flux

v chemical potential: BBN, LSS

v mass: tot, LSS,UHECR

v oscillations and magnetic moments: BBN

non-thermal effects: CMB, LSS,…


Neutrinos and BBNNew species couples to gravity and speed up expansion

3 H2 = 8 G

Neff: increasing the relativistic energy density speeds up the expansion and increases the 4He mass fraction Yp

is the only free parameter (standard scenario)

Baryons are now well constrained by CMB

bh2 = 0.023(2)

CMB + Deuterium

BBN

Cuoco et al 2004

)1/(4

1178 3/4

ReffN


1) chemical potentials contribute to Neff

2) a positive electron neutrino chemical potential (more neutrinos than antineutrinos) favour n p processes with respect to p n processes.

....7

157

303 4

4

2

2

i

iieffN

Dolgov et al 2002

Cuoco et al 2004


Neutrinos and CMBNeff affects the radiation-matter equality point

ISW: Integrated Sachs-Wolfe Effect on acoustic peaks

The large number of cosmological parameters does not allow for a stringent limit


Neutrinos and Large Scale Structuresneutrinos suppress inhomogeneities which grow for gravitational instability until they become nonrelativistic

mv=1.2 eVmv=2.3 eV

mv=4.6 eV

mv=6.9 eV

Key parameters:

MpchmeVl

eVmh

vv

nr

v

15.38

1.94

122/1

02



Decoupling and distortion

Residual v interactions at e+-e- annihilation stage produce non-thermal features

Kinetic eq. x=m a

)(11

1)(

)3(

)(1

34

xPae

xf

Pxxdxd

fCxH

fdxd

iixa

aa

Pi orthogonal polynomial for measure 1/exp(x)+1

f/ftherm

ka


No mixing: z=T a e x Neff

1.4 0.94% 0.43% 3.04

Effects of v oscillations

Description in terms of density matrix

Mangano et al 2002

Dolgov et al 2002

Mangano et al 2005 )(,282

2

CEmG

pMHpi

W

Fpt

E electron/positron energy density

Three regimes:

At high temperatures (x<0.3) oscillations suppressed by medium effects

When electron density (adiabatically) decreases:MSW regime

Vacuum oscillations driven by M2/p



No mixing: z=T a e x Neff

1.4 0.73% 0.52% 3.05

Result for s122=0.3, s23

2=0.5, s13=0, m2solar=8 10-5 eV2, m2

atm=2.2 10-3 eV2,

Very tiny effect

))019.04.21.24(101(1

1)(

))047.01.42.21(101(1

1)(

324

324

xxxe

xf

xxxe

xf

x

xe

Small effect on 4He mass fraction: Y=2 10-4


A model Cuoco, Lesgourgues, Mangano and Pastor 2005

Extra neutrinos from out of equilibrium decay of scalars after neutrino decoupling

In the instantaneous decay limit at TD )( DTH

22 2/*)(

2

22

211)(

xx

xa eAe

yxf

Non thermal features in neutrino distributions

Effects seen in CMB and LSS


*2

202

712099.0104.3

)3(3299.01

2.93

AyN

AeV

mh

eff

v

Bounds from BBN

particles (decoupled) should not contribute too much to the expansion rate H

A < 0.1 at 95% C.L.


Present constraints from CMB (WMAP+ACBAR+VSA+CBI) and LSS (2dFGRS+SDSS) + SNIa data (Riess et al.)

Model: standard CDM + nonthermal v’s

Cl and P(k) computed using CAMB code (Lewis and Challinor 2002)

Likelihoods (using COSMOMC Lewis and Bridle 2002))


Degeneracies:

DM, Neff and m0

Neff >4 not forbidden

by BBN !

Future perspectives:

can we remove the

degeneracy?


Forecast:

“conservative”: Planck+ SDSS

“ambitious”: CMBPOL+ 40 h-3 Gpc survey with kmax=0.1 h Mpc-1

m0 and vh2 (q) large degeneracy


If we add extra relativistic particles the situation gets even more involved

For each non thermal model there is a “twin” model with extra thermal relativistic particles, sharing the same value of Neff, vh2 but a different value of the neutrino mass scale.

Way to solve the degeneracy:

independent information on the absolute neutrino mass scale (beta decay experiments)

*2

202

712099.0104.3

)3(3299.01

2.93

AyN

AeV

mh

eff

v

NNeV

mh

eff

v

04.3 2.93'02

MpchmeVl vv

nr 15.3812

2/1


Summary

Too many neutrinos around:

Likely: purely thermal distribution which can be very hardly (or not at all) measured in the future

Unlikely but possible: exotic features in v distributions opening new perspectives for new physics

After all:

Neutrinos enjoy to falsify theoretical physicist expectations

Documents

G. Mangano 1 Relic Neutrino Distribution Gianpiero Mangano INFN, Sezione di Napoli Italy