Massive neutrinos and their impact on cosmology Paolo Serra in collaboration with R. Bean, Dept. of Astronomy, Ithaca, NY A. De La Macorra, Istituto de Fisica, UNAM, Mexico G. L. Fogli, E. Lisi, A. Marrone, Dipartimento di Fisica e Sezione INFN, Bari A. Melchiorri, Dipartimento di Fisica Universita’ “La Sapienza” e Sezione INFN, Rome A.Palazzo, J. Silk, R. Trotta, Astrophysics, Denis Wilkinson Building, Oxford A. Slosar Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Paolo Serra Physics Department University of Rome “La Sapienza”

Neutrinos in cosmology Neutrinos are the most abundant particles in the Universe after photons This means that they play a role in many different epochs and aspects of cosmology, for example: –Leptogenesis –Big bang nucleosynthesis –Structure formation

Neutrinos in cosmology Neutrinos have a great impact on the two most important observables in cosmology: CMB (Cosmic Microwave Background radiation) LSS (Large Scale Structures) For these arguments see talk by S. Pastor

So cosmology can help particle physics to constrain neutrino masses

Neutrino mass from Cosmology (reprinted from Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, Slosar, hep-ph/ ) see talk by A. Palazzo Data  m i 1. WMAP < 2.3 eV 2. WMAP+SDSS < 1.2 eV 3. WMAP+SDSS+SN Riess +HST+BBN < 0.78 eV 4. CMB+LSS+SN Astier < 0.75 eV 5. CMB+LSS+SN Astier +BAO < 0.58 eV 6. CMB+LSS+SN Astier +Ly-  (P. Mc Donald et. al, see talk by M. Viel ) < 0.21 eV 7. CMB+LSS+SN Astier +BAO+Ly-  < 0.17 eV

Constraints placed by different cosmological data-set on  in terms of standard deviations from the best fit in each case Reprinted from Fogli et al. hep-ph/

Some considerations WMAP data alone, in the cosmological framework considered, are able to constrain  m <2 eV at 95%. This limit, as already stated, is the most conservative The constraints on  m  tend to scale linearly adding several different data-set Including SDSS Lyman-  data dramatically improves the constraints on  m  up to   m <0.17 eV (case 7 considered);  this limit generates a tension with bounds on m  obtained  by the Heidelberg-Moscow experiment (Klapdor claim). In fact:

Reprinted from Fogli et al. hep-ph/

Solving the tension The laboratory bounds on m  could be due to new physics beyond the light Mayorana neutrinos or systematic in the mass matrix (see talk by Vogl this morning) Bounds derived from astrophysics (and physics) are always affected by many systematic uncertanties which could be not well estimated We don’t know the fundamental nature of the two most important ingredient of the standard cosmological model, say dark matter and dark energy: their possible unknown parameters and behaviours could solve these problems This means that we can always consider more complicated cosmological models to obtain consistency with laboratory data. In this case, an analysis based on Bayesian evidence could be very useful to assess the need for new parameters

Now particle physics can help cosmology to establish the best model

More complicated models We must remember that cosmological bounds are always model dependent ! Relaxing some hypothesis we can obtain different constraints on cosmological parameters (mostly looking for parameter degeneracies) We consider just two possibilities: 1.Relaxing the assumption w=-1 (P=-  2. Adding an extra background of relativistic particles

Our Analysis De La Macorra, Melchiorri, Serra, Bean astroph/0 astroph/ We analyzed the latest CMB, Galaxy Clusters, SNI-IA data with a dark energy parametrized with an equation of state: We restricted the analysis to three-flavour neutrino mixing with degenerate masses so that: We assume a cosmological model with primordial adiabatic and scalar invariant inflationary perturbations and with a prior on the sum of neutrino masses given by the Heidelberg-Moscow experiment, say:

Figura con la degenerazione....

Possible physical origin for w<-1 ? Phantom fields (Caldwell, astro-ph/ ) They have w<-1 but suffer of several theoretical problems: Big Rip, instability of Perturbations... Interacting dark energy Dark energy can interact with other particles, for example neutrinos. The main motivation for these possibility is that the dark energy scale is, comparable to the neutrino masses

Possibilities for an interacting dark energy Coupled neutrino-dark energy models predict an apparent equation of state w ap less than -1, even if the real equation of state is larger than -1 In general we can include an interaction between dark matter (or neutrinos) and  via the function f(  which gives an interacting dark matter energy density

Relaxing the assumption N =3 Models with massive neutrinos suppress power on small scales, the suppression beeing proportional to  P/P≈-8  /  m Adding relativistic particles further suppress power on scales smaller than the horizon at matter-radiation equality This means that, if the matter density is increased, there is parameter degeneracy between the number of relativistic species N  and the sum  m  of neutrino masses

Likelihood contours for the case of N neutrinos with equal masses, calculated from WMAP 2006+LSS, Melchiorri-Serra-Trotta, in preparation) H-M

Results A cosmological scenario based on a cosmological constant is unable to provide a good fit to current data when a massive neutrino component as large as suggested in the Heidelberg-Moscow experiment is included in the analysis A better fit to the data is obtained with a dark energy described with an equation of state At present, the Heidelberg-Moscow experiment is the only one able to esclude a cosmological constant at such high significance However, recent combined analysis with Lyman-alpha forest data seem to be in discord with the Heidelberg-Moscow result and, partially, also with the CMB. Future data will allow to solve these tension Cosmological results are always model dependent. Changing the number of relativistic particles is one possibility, but we can also think obout other ways.

Laboratory bounds on neutrino mass Experiments sensitive to absolute neutrino mass scale : Tritium beta decay: (Mainz) (Troitsk) Best fit gives a negative mass !!!

CMB Anisotropies (Spergel et al. 2006) Cosmological perturbations: The Observables

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. The relative lowering of the matter power spectrum is given by: But remember that, the most spectacular result in cosmology is: LOWERING OF THE MATTER POWER SPECTRUM

  /  (x)  power spectrum P(k) Percival et al. 02 Galaxy Surveys redshift surveys (2dF,SDSS) linear non-linear  /  1 60 Mpc bias uncertainty … Cosmological perturbations: The Observables

Neutrinos and the CMB The CMB is affected mostly by the number of neutrinos N  trough the Integrated Sachs-Wolfe effect) However, there are also (small) effects due to the mass of neutrinos

Effects of neutrinos on CMB and LSS (from Tegmark)

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

Parameter dependance of the luminosity distance

A brief explanation A classic result of the perturbation theory is that if all the matter contributing to the Cosmic density is able to cluster, the fluctuations grow as the Cosmic scale factor: If only a fraction    can cluster the equation is generalized to In the radiation dominated era p=0 and so we don’t have clustering. In the recent  -dominated epoch again, p=0. Fluctuations grow only in the matter dominated epoch.

In matter dominated era If all the matter contributing to the energy density can cluster we have: But if a fraction of matter is in form of massive neutrinos the situation is different. They contribute to the total energy density with a fraction f but they cluster only on scales bigger than the free- straming scale; for smaller scales they can’t do it, so we have:

From the entropy conservation we obtain that: The neutrino density today will be: That, for a massive neutrino, translates in an energy content given by:

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 scales. This lowering can be expressed by the formula (  and  m are degenerate!):  P/P≈-8  /  m

Cosmological Neutrinos Unfortunately, despite their high density, we can’t detect cosmological neutrinos directly (see Hagmann astro- ph/ for a discussion about future impossibilities). However, neutrinos have great impact on the two most important observables in cosmology: CMB (Cosmic Microwave Background radiation) LSS (Large Scale Structures)

Neutrino energy content in the universe In the early hot universe neutrinos are kept in equilibrium with the cosmic plasma through weak interaction reactions They decouple from the plasma when: At temperature the reaction increases the photon temperature respect to the neutrino temperature

From the entropy conservation we obtain that: The neutrino density today will be: That, for a massive neutrino, translates in an energy content given by:

The effects on CMB concern: Change of the position of the first peak with increasing neutrino masses Enhancement of the heights of the second and third acoustic peaks We don’t discuss here the physical origin of these effects, for a reference see, Ichikawa, Fukugita, Kawasaki, astro-ph/ Hu, Fukugita, Zaldarriaga, Tegmark Astrophys. J. 549, 669, 2001 In principle we can measure neutrino masses with CMB alone and this is very important: in fact, with respect to the large scale clustering data, we don’t have problems with possible unkown biasing and not well-controlled nonlinear effects

Neutrinos and Large Scale Structures Neutrinos affect the growth of cosmic clustering, so they can leave key imprints on the large scale structures we can see today In particular, massive neutrinos suppress the matter fluctuations on scales smaller than the their free-streaming scale when they becomes non-relativisitic. The result is a lowering of the matter power spectrum on scales smaller than the free streaming scales. This lowering can be expressed by the formula (  and  m are degenerate!):  P/P≈-8  /  m

...but we have degeneracies... Lowering the matter density suppresses the power spectrum This is virtually degenerate with non-zero neutrino mass

CMB anisotropies CMB Anisotropies are weakly affected by massive neutrinos. However they constrain very well the matter density and other parameters and, when combined with LSS data can break several degeneracies.

Phenomenological reason for this anticorrelation When  is increased  m must increase correspondingly in order to produce the same power spectrum (remember the degeneration betwenn   and  m ) However, we have the well known (  m,w) degeneracy coming from supernovae data (see the formula for the luminosity distance D L ) The combined effect is the anticorrelation in the plane  m  w

Overview Weighing neutrinos with cosmology and comparison with some laboratory data Impact of massive neutrinos on dark energy properties Conclusions and perspectives

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. The relative lowering of the matter power spectrum is given by:

Laboratory bounds on neutrino mass (for these arguments, see the talk by A. Palazzo) Experiments sensitive to absolute neutrino mass scale : Neutrinoless double beta decay (only if neutrino are Majorana particles!): Neutrinoless doule beta decay processes have been searched in many experiments with different isotopes, yielding negative results. Recently, members of the Heidelberg-Moscow experiment have claimed the detection of a  signal from the 76 Ge isotope. If the claimed signal is entirely due to a light Majorana neutrino masses then we have the constraint:

Overview Weighing neutrinos with cosmology and comparison with laboratory data Laboratory data constraints on massive neutrinos and their impact on cosmology and in particular on dark energy properties Conclusions and perspectives

Results (II) Several theoretical models have been recently proposed that can reproduce W<-1, as coupled neutrino-dark energy models. Moreover, the energy scale of dark energy is of the same order of the neutrino masses, so a possibly link between neutrinos and dark energy must certainly be further investigated Cosmological results are always model dependent. Changing the number of relativistic particles is one possibility, but we can also think obout other ways. What happen, for example, relaxing the flatness condition?

Constraints on a non-flat universe using CMB+SDSS+2dFGRS+supernovae data sets. Reprinted from Spergel et al. astro-ph/