Massive neutrinos and cosmology

TL;DR

This review surveys how free-streaming massive neutrinos imprint on cosmological perturbations, detailing the theoretical framework for perturbations with neutrinos, and summarizing current cosmological bounds on the sum of neutrino masses. It explains how neutrino masses modify the background evolution and suppress small-scale structure through free-streaming, and it assesses current constraints from CMB, galaxy surveys, and Lyα data, highlighting degeneracies with N_eff and other parameters. The article also outlines robust forecast methods (Fisher analyses) and discusses future techniques—CMB lensing, cosmic shear, BAO, and cluster counts—that promise sub-eV sensitivity, potentially enabling a detection of the minimal neutrino mass scale in favorable scenarios. Overall, it emphasizes the complementary role of cosmology and terrestrial experiments in pinning down the absolute neutrino mass scale and informs the design of future observational campaigns.

Abstract

The present experimental results on neutrino flavour oscillations provide evidence for non-zero neutrino masses, but give no hint on their absolute mass scale, which is the target of beta decay and neutrinoless double-beta decay experiments. Crucial complementary information on neutrino masses can be obtained from the analysis of data on cosmological observables, such as the anisotropies of the cosmic microwave background or the distribution of large-scale structure. In this review we describe in detail how free-streaming massive neutrinos affect the evolution of cosmological perturbations. We summarize the current bounds on the sum of neutrino masses that can be derived from various combinations of cosmological data, including the most recent analysis by the WMAP team. We also discuss how future cosmological experiments are expected to be sensitive to neutrino masses well into the sub-eV range.

Figures (23)

• Figure 1: The two neutrino schemes allowed if $\Delta m_{\rm atm}^2\gg \Delta m_{\rm sun}^2$: normal hierarchy (NH) and inverted hierarchy (IH).
• Figure 2: Expected values of neutrino masses according to the values in Eq. (\ref{['oscpardef']}). Left: individual neutrino masses as a function of the total mass for the best-fit values of the $\Delta m^2$. Right: ranges of total neutrino mass as a function of the lightest state within the $3\sigma$ regions (thick lines) and for a future determination at the $5\%$ level (thin lines).
• Figure 3: The upper (lower) lines are the frozen distortions of the electron (muon or tau) neutrino spectra as a function of the comoving momentum $y$, calculated with (solid) and without (dotted) the effect of flavour oscillations. Left: real neutrino distribution functions normalized to the equilibrium one. Right: contribution of the distortions to the comoving number density. Here the scale factor was normalized so that $a(t)\to 1/T_\gamma$ at large temperatures.
• Figure 4: Bounds on $N_{\rm eff}$ from BBN including D and $^4$He (contours at $68\%$ and $95\%$ CL) and from a combined analysis of BBN (D only) and CMB data. Here $\omega_{\rm b}=\Omega_{\rm b}h^2\simeq 10^{10}(\eta_{\rm b}/274)$. This Figure is taken from Ref. Cuoco:2003cu.
• Figure 5: Evolution of the background densities from the time when $T_{\nu}=1$ MeV (soon after neutrino decoupling) until now, for each component of a flat $\Lambda$MDM model with $h=0.7$ and current density fractions $\Omega_{\Lambda}=0.70$, $\Omega_{\rm b}=0.05$, $\Omega_{\nu}=0.0013$ and $\Omega_{\rm cdm}=1-\Omega_{\Lambda}-\Omega_{\rm b} -\Omega_{\nu}$. The three neutrino masses are distributed according to the Normal Hierarchy scheme (see Sec. \ref{['sec:numasses']}) with $m_1=0$, $m_2 = 0.009$ eV and $m_3 = 0.05$ eV. On the left plot we show the densities to the power $1/4$ (in eV units) as a function of the scale factor. On the right plot, we display the evolution of the density fractions (i.e., the densities in units of the critical density). We also show on the top axis the neutrino temperature (on the left in eV, and on the right in Kelvin units). The density of the neutrino mass states $\nu_2$ and $\nu_3$ is clearly enhanced once they become non-relativistic. On the left plot, we also display the characteristic times for the end of BBN and for photon decoupling or recombination.