# How to relax the cosmological neutrino mass bound

## TL;DR

This paper shows that the cosmological neutrino mass bounds are highly sensitive to the assumed neutrino momentum distribution, allowing for larger neutrino masses if their average momentum exceeds the thermal expectation.

## Contribution

It demonstrates that non-standard neutrino momentum distributions can significantly relax cosmological neutrino mass bounds, highlighting a degeneracy with $N_{\mathrm{eff}}$ and $m_{\nu}$.

## Key findings

- Neutrino distribution degenerates with $N_{\mathrm{eff}}$ and $m_{\nu}$ in observable effects.
- Mass bounds can be relaxed by a factor of two with larger average neutrino momentum.
- Current cosmological data cannot uniquely determine neutrino mass without assumptions on momentum distribution.

## Abstract

We study the impact of non-standard momentum distributions of cosmic neutrinos on the anisotropy spectrum of the cosmic microwave background and the matter power spectrum of the large scale structure. We show that the neutrino distribution has almost no unique observable imprint, as it is almost entirely degenerate with the effective number of neutrino flavours, $N_{\mathrm{eff}}$, and the neutrino mass, $m_{\nu}$. Performing a Markov chain Monte Carlo analysis with current cosmological data, we demonstrate that the neutrino mass bound heavily depends on the assumed momentum distribution of relic neutrinos. The message of this work is simple and has to our knowledge not been pointed out clearly before: Cosmology allows that neutrinos have larger masses if their average momentum is larger than that of a perfectly thermal distribution. Here we provide an example in which the mass limits are relaxed by a factor of two.