Early dark energy constraints with late-time expansion marginalization

Early dark energy (EDE) is an extension to the ΛCDM model that includes an additional energy density contribution near recombination. The model was proposed to reduce the tension between the measurements of the Hubble constant H₀ from the cosmic microwave background (CMB) and from the local cosmic distance ladder. Some analyses in the recent literature have shown intriguing hints for EDE. However, this model increases the tension in the derived clustering of galaxies (as measured by the so-called S₈ parameter) between CMB and large scale structure (LSS) measurements. This new tension limits the contribution of EDE during recombination, and thus its effect on the Hubble tension. In this work, we investigate whether the inclusion of a general, smooth late-time dark energy modification can increase back the EDE contribution when LSS data is included in the analysis. In order to generalize the late expansion with respect to the ΛCDM model, we substitute the cosmological constant by a late dark energy fluid model with a piecewise constant equation of state w(z) in redshift bins. We show that, when analysing this generalized model with combinations of CMB, LSS and type Ia supernovae data from several experiments no significant changes on S₈ and EDE parameter constraints is found. The contribution to the EDE fraction constraint with late-time expansion marginalization is f_EDE = 0.067⁺⁰₋₀.⁰¹⁹₀₂₇ using 3 redshift bins, with similar results for 5 and 10 redshift bins. This work shows that in order to solve simultaneously the Hubble and S₈ tensions, one needs a mechanism for increasing the clustering of matter at late times different from a simple change in the background evolution of late dark energy.