Cosmic Neutrino Background Detection in Large-Neutrino-Mass Cosmologies

The Cosmic Neutrino Background (CNB) is a definite prediction of the standard cosmological model and its direct discovery would represent a milestone in cosmology and neutrino physics. In this work, we consider the capture of relic neutrinos on a tritium target as a possible way to detect the CNB, as aimed for by the PTOLEMY project. Crucial parameters for this measurement are the absolute neutrino mass $m_\nu$ and the local neutrino number density $n_\nu^{\rm loc}$. Within the $\Lambda$CDM model, cosmology provides a stringent upper limit on the sum of neutrino masses of $\sum m_\nu < 0.12\,{\rm eV}$, with further improvements expected soon from galaxy surveys by DESI and EUCLID. This makes the prospects for a CNB detection and a neutrino mass measurement in the laboratory very difficult. In this context, we consider a set of non-standard cosmological models that allow for large neutrino masses ($m_\nu \sim 1\,{\rm eV}$), potentially in reach of the KATRIN neutrino mass experiment or upcoming neutrinoless double-beta decay searches. We show that the CNB detection prospects could be much higher in some of these models compared to those in $\Lambda$CDM, and discuss the potential for such a detection to discriminate between cosmological scenarios. Moreover, we provide a simple rule to estimate the required values of energy resolution, exposure, and background rate for a PTOLEMY-like experiment to cover a certain region in the $(m_\nu,\, n_\nu^{\rm loc})$ parameter space. Alongside this paper, we publicly release a code to calculate the CNB sensitivity in a given cosmological model.