Weighing neutrinos with Cosmology Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk hep-ph , PRD 71, , (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 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,  m 2 and  m 2 defined as follows: (m 1 2,m 2 2,m 3 2 ) =  2 +(-  m 2 /2, +  m 2 /2, ±  m 2 ) where : ●  fixes the absolute neutrino mass scale ● the sign ± stands for the normal or inverted neutrino mass hierarchies respectively. ● They indicate that:  m 2 = eV 2  m 2 = eV 2

Araki et al. hep-ex/ STATUS OF 1-2 MIXING (SOLAR + KAMLAND) STATUS OF 2-3 MIXING (ATMOSPHERIC + K2K) Maltoni et al. hep-ph/

Normal hierarchy Inverted hierarchy Moreover neutrino masses can also be degenerate SOLAR KAMLAND ATMO. K2K

Hovever: -They can't determine the absolute mass scale  -They can't determine the hierarchy ±  m 2 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 Neutrinos Neutrinos 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:

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  eVm  eV m  eVm  eV Ma ’96

A classical result of the perturbation theory is that: where :   = fraction of the total energy density which can cluster 

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 which Neutrino clustering is suppressed is called the neutrino free- streaming scale and roughly corresponds to the distance neutrinos have time to travel while the universe expands by a factor of 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 f   from Tegmark)

Neutrino mass from Cosmology DataAuthors  m i WMAP+2dFHannestad 03 < 1.0 eV SDSS+WMAPTegmark et al. 04 < 1.7 eV WMAP+2dF+SDSSCrotty et al. 04 < 1.0 eV WMAP+SDSS LyaSeljak et al. 04< 0.43 eV B03+WMAP+LSSMcTavish al. 05 < 1.2 eV 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  m h 2 from the CMB ● We constrain the parameter h from the HST

Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk hep-ph , PRD 71, , (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 0 2  results ● There is a partial, preliminar, tension also betwenn WMAP 3 years+SDSS results with 0 2  results ● Results are model dependent

Just an example...