Hubble tension in lepton asymmetric cosmology with an extra radiation

We study the fit of cosmological models with two additional free parameters $N_{\mathrm{eff}}$ and ${\xi }_e$ in addition to the parameters of $\mathrm{\Lambda }\mathrm{CDM}$. 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 $0.3\lesssim \mathrm{\Delta }{N}_{\mathrm{eff}}\lesssim 0.6$.

Figure 1

Effects of electron-type lepton asymmetry ${\xi }_e$ and the relativistic degrees of freedom $N_{\mathrm{eff}}$ on the helium abundance $Y_P$. A larger $N_{\mathrm{eff}}$ leads to a larger $Y_P$, while a larger ${\xi }_e$ suppresses the resulting $Y_P$. The shading rectangle illustrates the value of the $Y_P$ measurement: $Y_P=0.2449\pm 0.0040$ [43].

Figure 2

Posterior distributions of ${\mathrm{\Omega }}_b{h}^2$, $N_{\mathrm{eff}}$, $H_0$, $Y_P$, and ${\chi }_{\text{Aver}}^2$ on a $N_{\mathrm{eff}}$ model for several cases with different amount of lepton asymmetry. This posterior have been derived for all datasets ($\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{BBN}+\mathrm{R}19$).

Figure 3

Same as Fig. 2 for distant datasets ($\mathrm{CMB}+\mathrm{BAO}+\mathrm{BBN}$) only.