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The shorten sound horizon scale at the recombination epoch by introducingextra 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, anextra radiation model and an EDE and extra radiation co-existing model withpaying attention to the fit to big bang nucleosynthesis (BBN). We find that afit to BBN in EDE models also is somewhat poorer than that in the $\Lambda$CDMmodel, because the increased inferred baryon asymmetry leads to smallerdeuterium abundance. We find that an extra radiation-EDE co-existing modelindicates the largest present Hubble parameter $H_0$ between models studied. Wealso the examine data sets dependence, whether we include BBN or not. Thedifference in an extra radiation model is $3.22 < N_\mathrm{eff} < 3.49 \,(68\%)$ for data sets without BBN and $3.16 < N_\mathrm{eff} < 3.40 \,(68 \%)$ fordata sets with BBN, and is so large that the $1\sigma$ border of the largerside becomes the $2\sigma$ border.

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