Relic Neutrino Degeneracies and Their Impact on Cosmological Parameters

In the standard $\Lambda$CDM model, neutrinos are treated as radiation, with their masses and possible degeneracy ignored. In this paper, we compute the impact of a finite relic neutrino degeneracy $\xi$ on the CMB angular power spectra, and obtain constraints on $\xi$ using current cosmological data sets. We find that $\xi \approx O(1)$ is still allowed. We also study the correlations between $\xi$, the Hubble parameter $H_0$, and the spectral index $n_s$. Due to these correlations, the CMB constraints on inflation models are loosened when $\xi$ is fitted together with other cosmological parameters, such that some models excluded at 95% confidence level by standard fittings without $\xi$ could be revived. Furthermore, the tension in CMB and local measurements of $H_0$ is slightly alleviated. Our results suggest that $\xi$ is a non-negligible physical parameter for cosmological analyses.