Origin of cosmological neutrino mass bounds: background $\textit{versus}$ perturbations

TL;DR

This paper clarifies that cosmological neutrino mass bounds primarily measure the neutrino energy density evolution, distinguishing background effects from perturbation impacts, and shows the bound on perturbations is less restrictive.

Contribution

It explicitly separates background and perturbation effects of neutrino mass on cosmology, providing new insights into the physical origin of the neutrino mass bounds.

Findings

Neutrino mass bounds are mainly sensitive to background energy density.

The bound on perturbation effects is significantly relaxed.

Clarifies the physical interpretation of cosmological neutrino mass limits.

Abstract

The cosmological upper bound on the total neutrino mass is the dominant limit on this fundamental parameter. Recent observations-soon to be improved-have strongly tightened it, approaching the lower limit set by oscillation data. Understanding its physical origin, robustness, and model-independence becomes pressing. Here, we explicitly separate for the first time the two distinct cosmological neutrino-mass effects: the impact on background evolution, related to the energy in neutrino masses; and the "kinematic" impact on perturbations, related to neutrino free-streaming. We scrutinize how they affect CMB anisotropies, introducing two effective masses enclosing $\textit{background}$ ($\sum m_\nu^\mathrm{Backg.}$) and $\textit{perturbations}$ ($\sum m_\nu^\mathrm{Pert.}$) effects. We analyze CMB data, finding that the neutrino-mass bound is mostly a background measurement, i.e., how the neutrino energy density evolves with time. The bound on the "kinematic" variable $\sum m_\nu^\mathrm{Pert.}$ is largely relaxed, $\sum m_\nu^\mathrm{Pert.} < 0.8\,\mathrm{eV}$. This work thus adds clarity to the physical origin of the cosmological neutrino-mass bound, which is mostly a measurement of the neutrino equation of state, providing also hints to evade such a bound.