  Recent measurement of the primordial $^4$He abundance $Y_p$ from EMPRESS
suggests a cosmological scenario with the effective number of neutrino species
deviated from the standard value and non-zero lepton asymmetry. We argue that
the extension of the standard cosmological model would be more demanded when
the Hubble tension is taken into account, in which derived baryon density could
be somewhat higher than the standard $\Lambda$CDM framework. We also discuss
the issue by assuming early dark energy whose energy density can have a sizable
fraction at the epoch of big bang nucleosynthesis. We show that the existence
of early dark energy can reduce some tension implied by the EMPRESS $Y_p$
results.
