Cosmological aspects of neutrinos (II) Sergio Pastor (IFIC Valencia) JIGSAW 2007 TIFR Mumbai, February 2007 ν

Cosmological aspects of neutrinos 2nd & 3rd lectures Degenerate relic neutrinos (Neutrino asymmetries) Massive neutrinos as Dark Matter Effects of neutrino masses on cosmological observables Bounds on m ν from CMB, LSS and other data Bounds on the radiation content (N ν ) Future sensitivities on m ν and N ν from cosmology

Degenerate relic neutrinos (relic neutrino asymmetries)

T~MeV t~sec Primordial Nucleosynthesis Decoupled neutrinos (Cosmic Neutrino Background) Neutrinos coupled by weak interactions

Equilibrium thermodynamics Particles in equilibrium when T are high and interactions effective T~1/ a(t) Distribution function of particle momenta in equilibrium Thermodynamical variables VARIABLE RELATIVISTIC NON REL. BOSEFERMI

T~MeV t~sec Primordial Nucleosynthesis Neutrinos coupled by weak interactions    /T

Relic neutrino asymmetries Raffelt Fermi-Dirac spectrum with temperature T and chemical potential  More radiation

Degenerate Big Bang Nucleosynthesis If   0, for any flavor  (  )>  (0)   4 He Plus the direct effect on n  p if  ( e )  0  e >0   4 He Pairs  (  e,  N ) that produce the same observed abundances for larger  B Kang & Steigman 1992

Hansen et al 2001Hannestad 2003 Combined bounds BBN & CMB-LSS In the presence of flavor oscillations ? Degeneracy direction (arbitrary ξ e )

Flavor neutrino oscillations in the Early Universe Density matrix Mixing matrix Expansion of the Universe Charged lepton background (2nd order contribution) Collisions (damping) Neutrino background: diagonal and off-diagonal potentials Dominant term: Synchronized Neutrino Oscillations

BBN Evolution of neutrino asymmetries Effective flavor equilibrium (almost) established  Dolgov et al 2002 Wong 2002 Abazajian et al 2002 Serpico & Raffelt 2005

Massive Neutrinos and Cosmology

Relic neutrinos influence several cosmological epochs T < eVT ~ MeV Formation of Large Scale Structures LSS Cosmic Microwave Background CMB Primordial Nucleosynthesis BBN No flavour sensitivity N eff & m ν ν e vs ν μ,τ N eff

We know that flavour neutrino oscillations exist From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Evidence of Particle Physics beyond the Standard Model !

Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Mixing matrix U Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122 [hep-ph/ v5]

Mixing Parameters... From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122 [hep-ph/ v5]

... and neutrino masses Data on flavour oscillations do not fix the absolute scale of neutrino masses eV atm solar NORMAL INVERTED eV m0m0 What is the value of m 0 ?

Direct laboratory bounds on m ν Searching for non-zero neutrino mass in laboratory experiments Tritium beta decay: measurements of endpoint energy m( ν e ) < 2.2 eV (95% CL) Mainz Future experiments (KATRIN) m( ν e ) ~ eV Neutrinoless double beta decay: if Majorana neutrinos experiments with 76 Ge and other isotopes: Im ee I < 0.4h N eV

Absolute mass scale searches Neutrinoless double beta decay < eV Tritium β decay < 2.2 eV < eV Cosmology

Evolution of the background densities: 1 MeV → now photons neutrinos cdm baryons Λ m 3 =0.05 eV m 2 =0.009 eV m 1 ≈ 0 eV Ω i = ρ i /ρ crit

The Cosmic Neutrino Background Number density Energy density Massless Massive m ν >>T Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species At present 112 per flavour Contribution to the energy density of the Universe

Neutrinos as Dark Matter Neutrinos are natural DM candidates They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter First structures to be formed when Universe became matter -dominated Ruled out by structure formation CDM Neutrino Free Streaming Φ b, cdm ν

Neutrinos as Dark Matter Neutrinos are natural DM candidates They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter First structures to be formed when Universe became matter -dominated HDM ruled out by structure formation CDM

Neutrinos as Hot Dark Matter Effect of Massive Neutrinos: suppression of Power at small scales

Neutrinos as Hot Dark Matter Effect of Massive Neutrinos: suppression of Power at small scales

Neutrinos as Hot Dark Matter Massive Neutrinos can still be subdominant DM: limits on m ν from Structure Formation (combined with other cosmological data)

Cosmological observables accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration ? inflation RD (radiation domination)MD (matter domination) dark energy domination

Power Spectrum of density fluctuations Matter power spectrum is the Fourier transform of the two-point correlation function Field of density Fluctuations

Galaxy Redshift Surveys SDSS 2dFGRS ~ 1300 Mpc

Cosmological observables: LSS accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration ? inflation RD (radiation domination)MD (matter domination) dark energy domination 0<z<0.2 matter power spectrum P(k)  galaxy redshift surveys linear non-linear δρ/ρ<1 δρ/ρ ~ 1 60 Mpc bias uncertainty Distribution of large-scale structures at low z

Power spectrum of density fluctuations Bias b 2 (k)=P g (k)/P m (k) k ma x SDSS 2dFGRS Non-linearity

Cosmological observables : LSS accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration ? inflation RD (radiation domination)MD (matter domination) dark energy domination 2<z<3 Lyman- α forests in quasar spectra matter power spectrum P(k)  various systematics Distribution of large-scale structures at medium z

Neutrinos as Hot Dark Matter Effect of Massive Neutrinos: suppression of Power at small scales Massive Neutrinos can still be subdominant DM: limits on m ν from Structure Formation (combined with other cosmological data) ffνffν

Structure formation after equality baryons and CDM experience gravitational clustering

growth of  /  (k,t) fixed by « gravity vs. expansion » balance    a Structure formation after equality baryons and CDM experience gravitational clustering

neutrinos experience free-streaming with v = c or /m Structure formation after equality baryons and CDM experience gravitational clustering

neutrinos cannot cluster below a diffusion length  = ∫ v dt < ∫ c dt Structure formation after equality baryon and CDM experience gravitational clustering baryons and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or /m

o neutrinos cannot cluster below a diffusion length  = ∫ v dt < ∫ c dt for (2  /k) <, free-streaming supresses growth of structures during MD    a 1-3/5 f with f =   /  m ≈ (  m )/(15 eV) Structure formation after equality baryon and CDM experience gravitational clustering baryons and CDM experience gravitational clustering neutrinos experience free-streaming with v = c or /m

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/ ] Structure formation after equality  cdm bb   metric a Massless neutrinos

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/ ] Structure formation after equality  cdm bb   metric a 1-3/5f a Massive neutrinos f ν =0.1

Effect of massive neutrinos on P(k) Observable signature of the total mass on P(k) : P(k) massive P(k) massless various f f ν Lesgourgues & SP, Phys. Rep. 429 (2006) 307

Cosmological observables: CMB accélération décélération lente décélération rqpide accélération décélération lente décélération rqpide inflationradiationmatièreénergie noire acceleration slow deceleration fast deceleration ? inflation RD (radiation domination)MD (matter domination) dark energy domination z≈1100  photon power spectra CMB temperature/polarization anisotropies Anisotropies of the Cosmic Microwave Background

CMB TT DATA Multipole Expansion Map of CMBR temperature Fluctuations Angular Power Spectrum

CMB TT DATA Multipole Expansion Map of CMBR temperature Fluctuations Angular Power Spectrum

CMB Polarization DATA TT TE EE BB WMAP 3

Effect of massive neutrinos on the CMB spectra 1)Direct effect of sub-eV massive neutrinos on the evolution of the baryon-photon coupling is very small 2)Impact on CMB spectra is indirect: non-zero Ω ν today implies a change in the spatial curvature or other Ω i. The background evolution is modified Ex: in a flat universe, keep Ω Λ +Ω cdm +Ω b +Ω ν =1 constant

Effect of massive neutrinos on the CMB spectra Problem with parameter degeneracies: change in other cosmological parameters can mimic the effect of nu masses

Effect of massive neutrinos on the CMB and Matter Power Spectra Max Tegmark

End of 2nd lecture