  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 $0.3 \lesssim \Delta N_\mathrm{eff}
\lesssim 0.6$.
