Comparing early dark energy and extra radiation solutions to the Hubble tension with BBN

Abstract: The shorten sound horizon scale at the recombination epoch by introducing extra energy components such as the extra radiation or early dark energy (EDE) is a simple approach to so-called the Hubble tension. We compare EDE models, an extra radiation model and an EDE and extra radiation co-existing model with paying attention to the fit to big bang nucleosynthesis (BBN). We find that a fit to BBN in EDE models also is somewhat poorer than that in the $\Lambda$CDM model, because the increased inferred baryon asymmetry leads to smaller deuterium abundance. We find that an extra radiation-EDE co-existing model indicates the largest present Hubble parameter $H_0$ between models studied. We also the examine data sets dependence, whether we include BBN or not. The difference in an extra radiation model is $3.22 < N_\mathrm{eff} < 3.49 \,(68 \%)$ for data sets without BBN and $3.16 < N_\mathrm{eff} < 3.40 \,(68 \%)$ for data sets with BBN, and is so large that the $1\sigma$ border of the larger side becomes the $2\sigma$ border.