Current cosmological bounds on neutrino masses and relativistic relics

TL;DR

This study extends the standard flat ΛCDM cosmology to include an arbitrary number of massive neutrinos and extra relativistic relics, parameterized by the total mass $M$ and the effective number of relativistic species $N_{ m eff}$. By combining the latest CMB (WMAP, ACBAR) and LSS (2dF, SDSS) data with SN Ia and HST priors, the authors quantify how $M$ and $N_{ m eff}$ trade off against each other and how mass-splitting scenarios affect cosmological observables via neutrino free-streaming. They show that, for three degenerate neutrinos, the 2σ bound is $M<1.0$ eV with CMB+LSS data and tightens to $M<0.6$ eV when adding priors; when $N_{ m eff}$ is allowed to vary, the upper bound on $M$ spans roughly $1.0$–$1.5$ eV depending on the mass splitting. A key result is the robust separation of neutrino effects from primordial gravitational waves, indicating the neutrino mass limits are stable against the inclusion of tensor modes; degeneracies can be partially broken with external priors, and non-linear LSS corrections are essential for exploiting small-scale data. Overall, the work highlights how cosmology constrains the neutrino sector and sets the stage for tighter future limits with upcoming data.

Abstract

We combine the most recent observations of large-scale structure (2dF and SDSS galaxy surveys) and cosmic microwave anisotropies (WMAP and ACBAR) to put constraints on flat cosmological models where the number of massive neutrinos and of massless relativistic relics are both left arbitrary. We discuss the impact of each dataset and of various priors on our bounds. For the standard case of three thermalized neutrinos, we find an upper bound on the total neutrino mass sum m_nu < 1.0 (resp. 0.6) eV (at 2sigma), using only CMB and LSS data (resp. including priors from supernovae data and the HST Key Project), a bound that is quite insensitive to the splitting of the total mass between the three species. When the total number of neutrinos or relativistic relics N_eff is left free, the upper bound on sum m_nu (at 2sigma, including all priors) ranges from 1.0 to 1.5 eV depending on the mass splitting. We provide an explanation of the parameter degeneracy that allows larger values of the masses when N_eff increases. Finally, we show that the limit on the total neutrino mass is not significantly modified in the presence of primordial gravitational waves, because current data provide a clear distinction between the corresponding effects.

Figures (6)

• Figure 1: Two-dimensional likelihood in $(N_{\rm eff}, M)$ space, marginalized over the six remaining parameters of the model. We plot the 1$\sigma$ (green / dark) and 2$\sigma$ (yellow / light) allowed regions. Here we used CMB (WMAP & ACBAR) and LSS (2dF & SDSS) data, adding different external priors as defined in section \ref{['method_data']}: (a) no priors, (b) HST, (c) HST+SN99, (d) HST+SN03.
• Figure 2: Illustration of the main parameter degeneracy affecting our results. For three particular models, we plot on the left the CMB temperature spectrum (normalized to WMAP) and on the right the matter power spectrum (two of them have been rescaled by hand for clarity). See the main text for details.
• Figure 3: Impact of various assumptions related to the LSS data set. The default model for which we show 1$\sigma$ (dashed) and 2$\sigma$ (solid) contours was obtained with WMAP, ACBAR, 2dF, SDSS, plus the HST and SN99 priors. Each panel shows the 1$\sigma$ (green / dark) and 2$\sigma$ (yellow / light) allowed regions (a) when including the 2dF bias prior Peacock:2001gs, (b) without the SDSS data, (c) without the 2dF data, (d) without non-linear corrections.
• Figure 4: Matter power spectrum for the best-fit model with $(M, N_{\rm eff})=(0,3)$ , plotted with and without non-linear corrections. The difference becomes significant in the region $k > 0.15 \, h~{\rm Mpc}^{-1}$ probed by the last two points in the SDSS data set.
• Figure 5: 1$\sigma$ (green / dark) and 2$\sigma$ (yellow / light) allowed regions in ($M$, $N_{\rm eff}$) space, marginalized over the eight other free parameters of the flat $\Lambda$CDM+tensors model. For comparison, we show the contours corresponding to the case with no gravitational waves. The difference is very small, showing the ability of the data to make a clear difference between the effect of neutrinos and gravitational waves.