Abstract
We study the fit of cosmological models with two additional free parameters $N_\mathrm{eff}$ and $\xi_e$ in addition to the parameters of $\Lambda$CDM. We introduce extra radiation components such as hot axions or sterile neutrinos in addition to the energy density of neutrinos with large neutrino degeneracy. Then, a larger $N_\mathrm{eff}$ is allowed without spoiling Big Bang Nucleosynthesis (BBN), as positive neutrino degeneracy $\xi_e$ could improve BBN fit. By analysing the data from Planck, baryon acoustic oscillation (BAO), BBN and type-Ia supernovae (SNeIa), it can be seen that the Hubble tension can be ameliorated for $\xi_{e}\simeq 0.04$ and $0.3 \lesssim \Delta N_\mathrm{eff} \lesssim 0.6$.
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