Limits on the cosmic neutrino background

TL;DR

This paper reviews constraints on the cosmic neutrino background's overdensity, analyzing theoretical, experimental, and cosmological limits, and assesses the potential of future detection experiments to observe or distinguish neutrino properties.

Contribution

It provides the first comprehensive analysis of C$ u$B overdensity constraints across various neutrino masses and detection methods, including the effects of reference frame misalignment.

Findings

Pauli exclusion limits overdensities at small neutrino masses

Cosmology favors moderate overdensities between 0.2 and 3.5

Detection experiments can observe C$ u$B for neutrino masses above 50 meV

Abstract

We present the first comprehensive discussion of constraints on the cosmic neutrino background (C$\nu$B) overdensity, including theoretical, experimental and cosmological limits for a wide range of neutrino masses and temperatures. Additionally, we calculate the sensitivities of future direct and indirect relic neutrino detection experiments and compare the results with the existing constraints, extending several previous analyses by taking into account that the C$\nu$B reference frame may not be aligned with that of the Earth. The Pauli exclusion principle strongly disfavours overdensities $\eta_\nu \gg 1$ at small neutrino masses, but allows for overdensities $\eta_{\nu}\lesssim 125$ at the KATRIN mass bound $m_{\nu} \simeq 0.8\,\mathrm{eV}$. On the other hand, cosmology strongly favours $0.2 \lesssim \eta_{\nu} \lesssim 3.5$ in all scenarios. We find that direct detection proposals are capable of observing the C$\nu$B without a significant overdensity for neutrino masses $m_{\nu} \gtrsim 50\,\mathrm{meV}$, but require an overdensity $\eta_{\nu} \gtrsim 3\times 10^5$ outside of this range. We also demonstrate that relic neutrino detection proposals are sensitive to the helicity composition of the C$\nu$B, whilst some may be able to distinguish between Dirac and Majorana neutrinos.