Cosmological limits on neutrino unknowns versus low redshift priors

TL;DR

This paper investigates how low-redshift priors on $H_0$, the cluster mass bias $1-b$, and the reionization optical depth $\tau$ influence cosmological bounds on the active neutrino sum $\sum m_\nu$ and on extended models with $N_{\rm eff}$ and $m_s^{\rm eff}$. Using Planck 2015 data plus BAO and Planck SZ clusters, the authors perform MCMC analyses across three neutrino scenarios, demonstrating strong degeneracies between $\sum m_\nu$ and $H_0$ and highlighting the crucial role of polarization in constraining $N_{\rm eff}$. They show that allowing $1-b$ to vary freely yields the tightest $\sum m_\nu$ bound ($<0.126$ eV at 95% CL), while weak-lensing priors loosen the bound due to tensions in $\sigma_8$ measurements. A low-$\tau$ prior can push the bound down to about $0.099$ eV (95% CL) for certain data combinations, potentially approaching the inverted-hierarchy minimum and offering a cosmological avenue to probe neutrino mass ordering if astrophysical priors converge. Overall, the study advocates reporting results across multiple priors to avoid bias and underscores the continued strength of Planck+BAO as a baseline constraint in neutrino cosmology.

Abstract

Recent Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements from the Planck mission have significantly improved previous constraints on the neutrino masses as well as the bounds on extended models with massless or massive sterile neutrino states. However, due to parameter degeneracies, additional low redshift priors are mandatory in order to sharpen the CMB neutrino bounds. We explore here the role of different priors on low redshift quantities, such as the Hubble constant, the cluster mass bias, and the reionization optical depth $τ$. Concerning current priors on the Hubble constant and the cluster mass bias, the bounds on the neutrino parameters may differ appreciably depending on the choices adopted in the analyses. With regard to future improvements in the priors on the reionization optical depth, a value of $τ=0.05\pm 0.01$, motivated by astrophysical estimates of the reionization redshift, would lead to $\sum m_ν<0.0926$~eV at $90\%$~CL, when combining the full \textit{Planck} measurements, Baryon Acoustic Oscillation and Planck clusters data, thereby opening the window to unravel the neutrino mass hierarchy with existing cosmological probes.

Figures (5)

• Figure 1: $68\%$ and $95\%$ CL allowed regions in the ($\sum m_\nu$, $H_0$) plane illustrating the effect of the low redshift priors studied here.
• Figure 2: As Fig. \ref{['fig:fig1a']} panel but extending the neutrino mass model with $N_{\textrm{eff}}$ dark radiation species, illustrating the ($N_{\textrm{eff}}$, $H_0$) plane.
• Figure 3: $68\%$ and $95\%$ CL allowed regions in the ($\sum m_\nu$, $\sigma_8$) plane illustrating the effect of the low redshift priors studied here.
• Figure 4: $68\%$ and $95\%$ CL allowed regions in the ($\sum m_\nu$, $\sigma_8$) plane, focusing on the impact of the cluster mass bias prior.
• Figure 5: $68\%$ and $95\%$ CL allowed regions in the combined two-dimensional planes for the parameters $\Omega_{\textrm{c}}h^2$, $n_s$,$H_0$, $\sigma_8$ and $\tau$, together with their one-dimensional posterior probability distributions, arising from the combination of Planck pol plus BAO, Planck pol plus $H073p0$ and Planck pol plus SZ measurements.