Dark energy in light of recent DESI BAO and Hubble tension

It might be necessary to access the impact of recent released Dark Energy Spectroscopic Instrument (DESI) data on the state equation of dark energy in the Hubble-tension-free cosmologies. In this paper, we report the MCMC analysis for the w₀wₐCDM model with pre-recombination early dark energy (EDE) using Planck+DESI+Pantheon+SH0ES dataset. The results reveal that H₀=72.43± 0.75, w₀=-0.971±0.035, wₐ=-0.347±0.120 for axion-like EDE, while H₀=73.32± 0.64, w₀=-0.923±0.054, wₐ=-0.435±0.132 for AdS-EDE, and also not surprisingly the spectral index of primordial scalar perturbation moves towards nₛ=1. It looks like that in corresponding models the bestfit H₀ are higher than those with pre-DESI BAO data, but without the further exacerbation of S₈ tension.