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