Neutrino physics from cosmological observations

Abstract

We review the current status of neutrino cosmology, focusing mainly on the question of the absolute values of neutrino masses and the possibility of a cosmological neutrino lepton asymmetry. Neutrino massesThe absolute value of neutrino masses are very difficult to measure experimentally. On the other hand, mass differences between neutrino mass eigenstates, (m 1 , m 2 , m 3 ), can be measured in neutrino oscillation experiments. Observations of atmospheric neutrinos suggest a squared mass difference of δm 2 ≃ 3 × 10 −3 eV 2 [1,2]. While there are still several viable solutions to the solar neutrino problem the so-called large mixing angle solution gives by far the best fit with δm 2 ≃ 5×10 −5 eV 2 [3,4] (see also contributions by A. Hallin and A. Smirnov in the present volume).In the simplest case where neutrino masses are hierarchical these results suggest that m 1 ∼ 0, m 2 ∼ δm solar , and m 3 ∼ δm atmospheric . If the hierarchy is inverted [5-10] one instead finds m 3 ∼ 0, m 2 ∼ δm atmospheric , and m 1 ∼ δm atmospheric . However, it is also possible that neutrino masses are degenerate [11][12][13][14][15][16][17][18][19][20][21], m 1 ∼ m 2 ∼ m 3 ≫ δm atmospheric , in which case oscillation experiments are not useful for determining the absolute mass scale.Experiments which rely on kinematical effects of the neutrino mass offer the strongest probe of this overall mass scale. Tritium decay measurements have been able to put an upper limit on the electron neutrino mass of 2.2 eV (95% conf.) [22] (see also the contribution by Ch. Weinheimer in the present volume). However, cosmology at present yields an even stronger limit which is also based on the kinematics of neutrino mass.Neutrinos decouple at a temperature of 1-2 MeV in the early universe, shortly before electron-positron annihilation. Therefore their temperature is lower than the photon temperature by a factor (4/11) 1/3 . This again means that the total neutrino number density is related to the photon number density by n ν = 9 11 n γ (1)Massive neutrinos with masses m ≫ T 0 ∼ 2.4 × 10 −4 eV are non-relativistic at present and therefore contribute to the cosmological matter density [23][24][25]]calculated for a present day photon temperature T 0 = 2.728K. Here, m ν = m 1 + m 2 + m 3 . However, because they are so light these neutrinos free stream on a scale of roughly k ≃ 0.03m eV Ω 1/2 m h Mpc −1 [26][27][28]. Below this scale neutrino perturbations are completely erased and therefore the matter power spectrum is suppressed, roughly by ∆P/P ∼ −8Ω ν /Ω m [28].This power spectrum suppression allows for a determination of the neutrino mass from measurements of the matter power spectrum on large scales. This matter spectrum is related to the galaxy correlation spectrum measured in large scale structure (LSS) surveys via the bias parameter, b 2 ≡ P g (k)/P m (k). Such analyses have been performed several times before [29,30], most recently using data from the 2dF galaxy survey [31]. This investigation finds an upper limit of 1.8-2.2 eV for the sum of neutrin...