Weighing neutrinos with Cosmology

Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk hep-ph 0408045, PRD 71, 123521, (2005)

Paolo Serra Physics Department

University of Rome “La Sapienza”

“Theoretical” neutrinos • 3 neutrinos, corresponding to 3 families of leptons• Electron, muon, and tau neutrinos• They are massless because we see only left-

handed neutrinos.• If not they are not necessarily mass eigenstates

(Pontecorvo): one species can “oscillate” into another

0iHtee Only if masses are non-zero

1) Sun

2) Cosmic Rays hitting the atmosphere

Two Obvious Sources of neutrinos

SuperKamiokande

SNO

Neutrino oscillation experiments

● Are sensitive to two independent squared mass difference, m2 and m2 defined as follows:

(m12,m2

2,m32) =2+(-m2/2, +m2/2, ±m2)

where :● fixes the absolute neutrino mass scale ● the sign ± stands for the normal or inverted neutrino mass hierarchies respectively.● They indicate that: m2=8•10-5 eV2

m2=2.4•10-3 eV2

Araki et al. hep-ex/0406035

STATUS OF 1-2 MIXING

(SOLAR + KAMLAND)

STATUS OF 2-3 MIXING (ATMOSPHERIC + K2K)

Maltoni et al. hep-ph/0405172

Normal hierarchy

Inverted hierarchy

Moreover neutrino masses can also be degenerate

catmospheri321 ,, mmmm

SOLAR KAMLAND

ATMO. K2K

123 mmm 312 mmm

Hovever:-They can't determine the absolute mass scale -They can't determine the hierarchy ±m2

To measure the parameter we need non oscillatory neutrino experiments. Current bounds on neutrino mass come from:

● Tritium decay: m<1.8 eV (2) (Maintz-

Troisk)● Neutrinoless 2 decay:

0.17 eV < m<2.0 eV (3) (Heidelberg-Moscow)

Cosmological NeutrinosNeutrinos are in equilibrium with the primeval plasma through weak interaction reactions. They decouple from the plasma at a temperature

We then have today a Cosmological Neutrino Background at a temperature:

With a density of:

That, for a massive neutrino translates in:

MeVTdec 1

eVkTKTT 43/1

1068.1945.1114

33,

32 1121827.0)3(

43 cmTnTgn

kkfff

eV

mh

eVm

h

mnk

kk

c

kk

kk

2.932.931 2

2,

Neutrinos in cosmology● Neutrinos affect the growth of cosmic

clustering, so they can leave key imprints on the cosmological observables

● In particular, massive neutrinos suppress the matter fluctuations on scales smaller than the their free-streaming scale.

m eV m eV

m eV m eV Ma ’96

A classical result of the perturbation

theory is that:

where:

= fraction of the total energy density which can cluster

pa

4

1241 p

In radiation dominated era: =0 so p=0 and the perturbation growth is suppressed

In matter dominated era:if all the matter contributing to the energy density is able to cluster:

so p=1 and the perturbation grows as the scale factor

but if a fraction of matter is in form of

neutrinos, the situation is different. In fact:

They contribute to the total energy density with a fraction f but they cluster only on scales bigger than the free-streaming scale; for smaller scales, they can't do it, so we must have:

=1-f for which: p<1 And the perturbation grows less than the scale factor The result is a lowering of the matter power spectrum on scales smaller than the free-streaming scale. The lowering can be expressed by the formula: P/P≈-8/m

The lenght scale below whichNeutrino clustering is suppressedis called the neutrino free-streamingscale and roughly corresponds to thedistance neutrinos have time to travelwhile the universe expands by a factorof two. Neutrinos will clearly not cluster in an overdense clump so small that its escape velocity is much smaller than typical neutrino velocity. On scales much larger than the free streaming scale, on the other hand,Neutrinos cluster just as cold dark matter.This explains the effects on the power spectrum.

Shape of the angular and the matter

power spectrum with varying

ffrom Tegmark)

Neutrino mass from Cosmology

Data Authors mi

WMAP+2dF Hannestad 03 < 1.0 eV

SDSS+WMAP Tegmark et al. 04 < 1.7 eV

WMAP+2dF+SDSS Crotty et al. 04 < 1.0 eV

WMAP+SDSS Lya Seljak et al. 04 < 0.43 eV

B03+WMAP+LSS McTavish al. 05 < 1.2 eV

All upper limits 95% CL, but different assumed priors !All upper limits 95% CL, but different assumed priors !

Our Analysis● We constrain the lowering P/P≈-8/m

from large scale structure data (SDSS+2df+Ly-)

● We constrain the parameter mh2 from the

CMB

● We constrain the parameter h from the

HST

Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk

hep-ph 0408045, PRD 71, 123521, (2005)● We analized the CMB (WMAP 1 year data),

galaxy clusters, Lyman-alpha (SDSS), SN-1A data in order to constrain the sum of neutrino mass in cosmology

● We restricted the analysis to three-flavour neutrino mixing

● We assume a flat -cold dark matter model with primordial adiabatic and scalar invariant inflationary perturbations

Results

● m ≤1.4 eV (2) (WMAP 1 year data +SDSS+ 2dFGRS)

● m ≤0.45 eV (2) (WMAP 1

year data+SDSS+2dFGRS+Ly )

What changes with new WMAP data ?

Doing a new, PRELIMINAR, analysis of the 3

years WMAP data, with SDSS and HST data , we

obtain:● m ≤ 0.8 eV (2)

Conclusions● Cosmological constraints on neutrino

mass are rapidly improving (our analysis on 1 year WMAP data indicated that m

≤1.4 eV, with the 3 years WMAP data the upper bound is m ≤0.8 eV)

● If one consider WMAP 1 year data+Ly then m ≤0.5 eV and there is a tension with 02 results

● There is a partial, preliminar, tension also betwenn WMAP 3 years+SDSS results with 02 results

● Results are model dependent

Just an example...