Constraining early dark energy with large-scale structure

An axion-like field comprising 10% of the energy density of the Universe near matter-radiation equality is a candidate to resolve the Hubble tension; this is the ``early dark energy'' (EDE) model. However, as shown in Hill et al. , the model fails to simultaneously resolve the Hubble tension and maintain a good fit to both cosmic microwave background (CMB) and large-scale structure (LSS) data. Here, we use redshift-space galaxy clustering data to sharpen constraints on the EDE model. We perform the first EDE analysis using the full-shape power spectrum likelihood from the Baryon Oscillation Spectroscopic Survey (BOSS), based on the effective field theory (EFT) of LSS. The inclusion of this likelihood in the EDE analysis yields a 25% tighter error bar on H₀ compared to primary CMB data alone, yielding H₀=68. 54-₀. ₉₅^+0. 52 km/s/Mpc (68% C. L. ). In addition, we constrain the maximum fractional energy density contribution of the EDE to f₄₃₄<0. 072 (95% C. L. ). We explicitly demonstrate that the EFT BOSS likelihood yields much stronger constraints on EDE than the standard BOSS likelihood. Including further information from photometric LSS surveys, the constraints narrow by an additional 20%, yielding H₀=68. 73-₀. ₆₉^+0. 42 km/s/Mpc (68% C. L. ) and f₄₃₄<0. 053 (95% C. L. ). These bounds are obtained without including local-Universe H₀ data, which is in strong tension with the CMB and LSS, even in the EDE model. We also refute claims that Markov-chain Monte Carlo analyses of EDE that omit SH0ES from the combined dataset yield misleading posteriors. Finally, we show that upcoming Euclid/DESI-like spectroscopic galaxy surveys will greatly improve the EDE constraints. We conclude that current data preclude the EDE model as a resolution of the Hubble tension, and that future LSS surveys can close the remaining parameter space of this model.