Canonical Hubble-Tension-Resolving Early Dark Energy Cosmologies Are Inconsistent with the Lyman-α Forest

Current cosmological data exhibit discordance between indirect and some direct inferences of the present-day expansion rate H_{0}. Early dark energy (EDE), which briefly increases the cosmic expansion rate prior to recombination, is a leading scenario for resolving this "Hubble tension" while preserving a good fit to cosmic microwave background (CMB) data. However, this comes at the cost of changes in parameters that affect structure formation in the late-time universe, including the spectral index of scalar perturbations n_{s}. Here, we present the first constraints on axionlike EDE using data from the Lyman-α forest, i.e., absorption lines imprinted in background quasar spectra by neutral hydrogen gas along the line of sight. We consider two independent measurements of the one-dimensional Lyα forest flux power spectrum from the Sloan Digital Sky Survey (SDSS eBOSS) and from the MIKE/HIRES and X-Shooter spectrographs. We combine these with a baseline dataset comprised of Planck CMB data and baryon acoustic oscillation (BAO) measurements. Combining the eBOSS Lyα data with the CMB and BAO dataset reduces the 95% confidence level (C.L.) upper bound on the maximum fractional contribution of EDE to the cosmic energy budget f_{EDE} from 0.07 to 0.03 and constrains H_{0}=67.9_{-0.4}^{+0.4}  km/s/Mpc (68% C.L.), with maximum a posteriori value H_{0}=67.9  km/s/Mpc. Similar results are obtained for the MIKE/HIRES and X-Shooter Lyα data. Our Lyα-based EDE constraints yield H_{0} values that are in >4σ tension with the SH0ES distance-ladder measurement and are driven by the preference of the Lyα forest data for n_{s} values lower than those required by EDE cosmologies that fit Planck CMB data. Taken at face value, the Lyα forest severely constrains canonical EDE models that could resolve the Hubble tension.