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

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 $\text{background}$ ($\sum m_{\hat{I}}{½}^{Backg.}$) and $\text{perturbations}$ ($\sum m_{\hat{I}}{½}^{Pert.}$) 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 $\sum m_{\hat{I}}{½}^{Pert.}$ is largely relaxed, $\sum m_{\hat{I}}{½}^{Pert.}<0.8\mathrm{eV}$. 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.

8 pages, 5 figures + Appendices. Minor clarifications and a discussion about the lensing anomaly added. Matches version accepted by JCAP