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

A shorter sound horizon scale at the recombination epoch, arising from introducing extra energy components such as extra radiation or early dark energy (EDE), is a simple approach to resolving the so-called Hubble tension. We compare EDE models, an extra radiation model, and a model in which EDE and extra radiation coexist, paying attention to the fit to big bang nucleosynthesis (BBN). We find that the fit to BBN in EDE models is somewhat poorer than that in the model, because the increased inferred baryon asymmetry leads to a smaller deuterium abundance. We find that an extra radiation--EDE coexistence model gives the largest present Hubble parameter H₀ among the models studied. We also examine the differences between the results obtained with and without consideration of the BBN. The difference in the extra radiation model is 3. 22<N₄₅₅<3. 49 (68%) for data sets without BBN and 3. 16<N₄₅₅<3. 40 (68%) for data sets with BBN, which is so large that the 1 border of the larger side becomes the 2 border.