Neutrino mass tension or suppressed growth rate of matter perturbations?

Abstract: Assuming a minimal $\Lambda$CDM cosmology with three massive neutrinos, the joint analysis of Planck cosmic microwave background data, DESI baryon acoustic oscillations, and distance moduli measurements of Type Ia supernovae from the Pantheon+ sample sets an upper bound on the total neutrino mass, $\sum m_\nu \lesssim 0.06$-$0.07$ eV, that lies barely above the lower limit from oscillation experiments. These constraints are mainly driven by mild differences in the inferred values of the matter density parameter across different probes that can be alleviated by introducing additional background-level degrees of freedom (e.g., by dynamical dark energy models). However, in this work we explore an alternative possibility. Since both $\Omega_\mathrm{m}$ and massive neutrinos critically influence the growth of cosmic structures, we test whether the neutrino mass tension may originate from the way matter clusters, rather than from a breakdown of the $\Lambda$CDM expansion history. To this end, we introduce the growth index $\gamma$, which characterizes the rate at which matter perturbations grow. Deviations from the standard $\Lambda$CDM value ($\gamma \simeq 0.55$) can capture a broad class of models, including non-minimal dark sector physics and modified gravity. We show that allowing $\gamma$ to vary significantly relaxes the neutrino mass bounds to $\sum m_\nu \lesssim 0.13$-$0.2$ eV, removing any tension with terrestrial constraints without altering the inferred value of $\Omega_\mathrm{m}$. However, this comes at the cost of departing from standard growth predictions: to have $\sum m_\nu \gtrsim 0.06$ eV one needs $\gamma > 0.55$, and we find a consistent preference for $\gamma > 0.55$ at the level of $\sim 2\sigma$. This preference increases to $\sim 2.5$-$3\sigma$ when a physically motivated prior $\sum m_\nu \ge 0.06$ eV from oscillation experiments is imposed.