Scale and redshift dependent limits on cosmic neutrino properties

Abstract

Cosmological neutrino mass and abundance measurements are reaching unprecedented precision. Testing their stability versus redshift and scale is a crucial issue, as it can serve as a guide for optimizing ongoing and future searches. Here, we perform such analyses, considering a number of redshift, scale, and redshift-and-scale nodes. Concerning the $k$-space analysis of $\sum m_{\nu }$, CMB observations are crucial, as they lead the neutrino mass constraints. Interestingly, some data combinations suggest a non-zero value for the neutrino mass with $2\sigma$ significance. The most constraining bound we find is $\sum m_{\nu }<0.54$ eV at $95\%$ CL in the $[10^{-3},10^{-2}]$ $h$/Mpc $k$-bin, a limit that barely depends on the data combination. Regarding the redshift- and scale-dependent neutrino mass constraints, high redshifts ($z>100$) and scales in the range $[10^{-3},10^{-1}]$ $h$/Mpc provide the best constraints. The least constraining bounds are obtained at very low redshifts $[0,0.5]$ and also at very small scales ($k>0.1h$/Mpc), due to the absence of observations. Highly relevant is the case of the $[100,1100]$, $[10^{-2},10^{-1}]$ $h$/Mpc redshift-scale bin, where a $2$-$3\sigma$ evidence for a non-zero neutrino mass is obtained for all data combinations. The bound from CMB alone at $68\%$ CL is $0.63_{-0.24}^{+0.20}$ eV, and the one for the full dataset is $0.56_{-0.23}^{+0.20}$ eV, clearly suggesting a non-zero neutrino mass at these scales, possibly related to a deviation of the ISW amplitude in this redshift range. Concerning the analysis of $N_{\mathrm{eff}}$ in the $k$-space, at intermediate scales ranging from $k=10^{-3}$ $h$/Mpc to $k=10^{-1}$ $h$/Mpc, accurate CMB data provide very strong bounds, the most robust one being $N_{\mathrm{eff}}=3.09\pm 0.14$, comparable to the standard expected value without a $k$-bin analysis. [abridged]

16 pages, 8 figures, 5 tables. Version accepted for publication in PRD

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