Cosmological constraints on early dark energy from the full shape analysis of eBOSS DR16

We evaluate the effectiveness of Early Dark Energy (EDE) in addressing the Hubble tension using data from the completed eBOSS survey, focusing on luminous red galaxies (LRGs), quasars (QSOs), and emission line galaxies (ELGs). We perform cosmological parameter measurements based on full shape analysis of the power spectrum of all three tracers. We conduct this full shape analysis with the effective field theory of large-scale structure (EFTofLSS). EDE is known to strongly suffer from volume projection effects, which makes the interpretation of cosmological constraints challenging. To quantify the volume projection effects within an EDE full shape analysis, we explore the impact of different prior choices on the nuisance parameters of EFTofLSS through an extensive mock study. We compare classical Gaussian priors to the non-informative Jeffreys prior, known to mitigate volume projection effects in ΛCDM. Our full shape analysis combines eBOSS and BOSS data with Planck, external Baryon Acoustic Oscillation (BAO), PantheonPlus, and SH0ES supernova data. EDE demonstrates to reduce the tension from 5.2σ to 3σ compared to ΛCDM. The derived values at a 68% credible interval with Gaussian and Jeffreys priors are H_0=71.73_-0.86^+0.82 km/s/Mpc with f_EDE = 0.1179_-0.022^+0.025 and H_0=72.03_-0.87^+0.82 km/s/Mpc with f_EDE = 0.1399_-0.022^+0.023, respectively. Although the Hubble tension is mitigated compared to ΛCDM, the inclusion of eBOSS data amplifies the tension within EDE from 2σ to 3σ, in contrast to the full shape analysis of BOSS data with Planck, external BAO, PantheonPlus, and SH0ES. This highlights the significance of incorporating additional large-scale structure data in discussions concerning models aiming to resolve the Hubble tension.