Neutron Stars as a Probe of Cosmic Neutrino Background

The Cosmic Neutrino Background (C$\nu$B) constitutes the last observable prediction of the standard cosmological model, which has yet to be detected directly. In this work, we show how the coherent scattering of neutrinos off dense neutron matter can lead to an additional cooling channel in neutron stars (NSs). We also include the effects of gravitational capture and boosting, but find that the cooling is efficient only in the presence of large overdensities. We further discuss the prediction of a boosted C$\nu$B flux on Earth from nearby NSs and the potential detection prospects in the case of a future nearby galactic supernova. Although currently these ideas do not offer any detection prospects, they can be used to constrain overdensities $\eta \lesssim {10}^{11}\text{-}{10}^{14}$ on short length scales $\mathcal{O}(10\text{ km})$. We also discuss the impact of new physics scenarios, such as long-range forces, on NS cooling through the C$\nu$B.