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Cosmological Aspects of Neutrino Physics (I) Sergio Pastor (IFIC) 61st SUSSP St Andrews, August 2006 Slide 2 Cosmological Aspects of Neutrino Physics 1st lecture Introduction: neutrinos and the History of the Universe Slide 3 This is a neutrino! Slide 4 T~MeV t~sec Primordial Nucleosynthesis Decoupled neutrinos (Cosmic Neutrino Background or CNB) Neutrinos coupled by weak interactions Slide 5 At least 1 species is NR Relativistic neutrinos T~eV Neutrino cosmology is interesting because Relic neutrinos are very abundant: The CNB contributes to radiation at early times and to matter at late times (info on the number of neutrinos and their masses) Cosmological observables can be used to test non-standard neutrino properties Slide 6 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 e vs , N eff Slide 7 Basics of cosmology: background evolution 1st lecture Introduction: neutrinos and the History of the Universe Relic neutrino production and decoupling Cosmological Aspects of Neutrino Physics Neutrinos and Primordial Nucleosynthesis Neutrino oscillations in the Early Universe* * Advanced topic Slide 8 Cosmological Aspects of Neutrino Physics 2nd & 3rd lectures Degenerate relic neutrinos (Neutrino asymmetries)* Massive neutrinos as Dark Matter Effects of neutrino masses on cosmological observables Bounds on m from CMB, LSS and other data Bounds on the radiation content (N ) Future sensitivities on m and N from cosmology * Advanced topic Slide 9 Suggested References Books Modern Cosmology, S. Dodelson (Academic Press, 2003) The Early Universe, E. Kolb & M. Turner (Addison-Wesley, 1990) Kinetic theory in the expanding Universe, Bernstein (Cambridge U., 1988) Recent reviews Neutrino Cosmology, A.D. Dolgov, Phys. Rep. 370 (2002) 333-535 [hep-ph/0202122] Massive neutrinos and cosmology, J. Lesgourgues & SP, Phys. Rep. 429 (2006) 307-379 [astro-ph/0603494] Primordial Neutrinos, S. Hannestad hep-ph/0602058 BBN and Physics beyond the Standard Model, S. Sarkar Rep. Prog. Phys. 59 (1996) 1493-1610 [hep-ph/9602260] Slide 10 Eqs in the SM of Cosmology The FLRW Model describes the evolution of the isotropic and homogeneous expanding Universe a(t) is the scale factor and k=-1,0,+1 the curvature Einstein eqs Energy-momentum tensor of a perfect fluid Slide 11 Eqs in the SM of Cosmology Eq of state p= = const a -3(1+) Radiation =1/3 Matter =0Cosmological constant =-1 R ~ 1/a 4 M ~1/a 3 ~const 00 component (Friedmann eq) H(t) is the Hubble parameter =M+R+=M+R+ crit =3H 2 /8G is the critical density = / crit Slide 12 Evolution of the Universe acclration dclration lente dclration rqpide acclration dclration lente dclration rqpide inflationradiationmatirenergie noire acceleration slow deceleration fast deceleration ? inflation RD (radiation domination)MD (matter domination) dark energy domination a (t)~t 1/2 a (t)~t 2/3 a (t)~e Ht Slide 13 Evolution of the background densities: 1 MeV now 3 neutrino species with different masses Slide 14 Evolution of the background densities: 1 MeV now photons neutrinos cdm baryons m 3 =0.05 eV m 2 =0.009 eV m 1 0 eV i = i / crit Slide 15 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 Slide 16 T~MeV t~sec Primordial Nucleosynthesis Neutrinos coupled by weak interactions (in equilibrium) Slide 17 T = T e = T 1 MeV T m Neutrinos in Equilibrium Slide 18 Neutrino decoupling As the Universe expands, particle densities are diluted and temperatures fall. Weak interactions become ineffective to keep neutrinos in good thermal contact with the e.m. plasma Rate of weak processes ~ Hubble expansion rate Rough, but quite accurate estimate of the decoupling temperature Since e have both CC and NC interactions with e T dec ( e ) ~ 2 MeV T dec ( , ) ~ 3 MeV Slide 19 T~MeV t~sec Free-streaming neutrinos (decoupled) Cosmic Neutrino Background Neutrinos coupled by weak interactions (in equilibrium) Neutrinos keep the energy spectrum of a relativistic fermion with eq form Slide 20 At T~m e, electron- positron pairs annihilate heating photons but not the decoupled neutrinos Neutrino and Photon (CMB) temperatures Slide 21 At T~m e, electron- positron pairs annihilate heating photons but not the decoupled neutrinos Neutrino and Photon (CMB) temperatures Photon temp falls slower than 1/a(t) Slide 22 Number density Energy density Massless Massive m >>T Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species The Cosmic Neutrino Background Slide 23 Number density Energy density Massless Massive m >>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 Slide 24 At T Effect of neutrinos on BBN 1. N eff fixes the expansion rate during BBN (N eff )> 0 4 He Burles, Nollett & Turner 1999 3.43.2 3.0 2. Direct effect of electron neutrinos and antineutrinos on the n-p reactions Slide 39 BBN: allowed ranges for N eff Cuoco et al, IJMP A19 (2004) 4431 [astro-ph/0307203] Using 4 He + D data (2) Slide 40 Neutrino oscillations in the Early Universe Neutrino oscillations are effective when medium effects get small enough Compare oscillation term with effective potentials Strumia & Vissani, hep-ph/0606054 Oscillation term prop. to m 2 /2E First order matter effects prop. to G F [n(e - )-n(e + )] Second order matter effects prop. to G F (E/M Z ) 2 [n(e - )+n(e + )] Coupled neutrinos Slide 41 Flavor neutrino oscillations in the Early Universe Standard case: all neutrino flavours equally populated oscillations are effective below a few MeV, but have no effect (except for mixing the small distortions f ) Cosmology is insensitive to neutrino flavour after decoupling! Non-zero neutrino asymmetries: flavour oscillations lead to (almost) equilibrium for all Slide 42 What if additional, sterile neutrino species are mixed with the flavour neutrinos? If oscillations are effective before decoupling: the additional species can be brought into equilibrium: N eff =4 If oscillations are effective after decoupling: N eff =3 but the spectrum of active neutrinos is distorted (direct effect of e and anti- e on BBN) Active-sterile neutrino oscillations Results depend on the sign of m 2 (resonant vs non-resonant case) Slide 43 Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq Flavour neutrino spectrum depleted Slide 44 Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq Flavour neutrino spectrum depleted Kirilova, astro-ph/0312569 Slide 45 Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq Flavour neutrino spectrum depleted Slide 46 Active-sterile neutrino oscillations Dolgov & Villante, NPB 679 (2004) 261 Additional neutrino fully in eq Slide 47 End of 1st lecture