Canonical Hubble-Tension-Resolving Early Dark Energy Cosmologies Are Inconsistent with the Lyman-$\alpha$ 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-$\alpha$ 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 $\mathrm{Ly}\alpha$ 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 $\mathrm{Ly}\alpha$ 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 $f_{\mathrm{EDE}}$ from 0.07 to 0.03 and constrains $H_0={67.9}_{-0.4}^{+0.4}\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ (68% C.L.), with maximum a posteriori value $H_0=67.9\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. Similar results are obtained for the MIKE/HIRES and X-Shooter $\mathrm{Ly}\alpha$ data. Our $\mathrm{Ly}\alpha$-based EDE constraints yield $H_0$ values that are in $>4\sigma$ tension with the SH0ES distance-ladder measurement and are driven by the preference of the $\mathrm{Ly}\alpha$ forest data for $n_s$ values lower than those required by EDE cosmologies that fit Planck CMB data. Taken at face value, the $\mathrm{Ly}\alpha$ forest severely constrains canonical EDE models that could resolve the Hubble tension.

Figure 1

Comparison of the best-fit linear matter power spectrum at $z_p=3$ from the EDE (gray) and $\mathrm{\Lambda }\mathrm{CDM}$ (orange) fits to the baseline $\mathrm{CMB}+\mathrm{BAO}$ dataset with the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ cosmologies for the eBOSS (blue) [30] and XQ-100 (red) $\mathrm{Ly}\alpha$ forest datasets. Shaded bands indicate the 68% C.L. from our baseline analyses; note that the best-fit EDE model lies outside the 68% C.L. due to prior-volume effects. The inset shows the slope $(d\ln P_{\mathrm{lin}}(k,z)/d\ln k){|}_{(k_p,z_p)}$, and the vertical line shows the $\mathrm{Ly}\alpha$ pivot wave number ($k_p=0.009\mathrm{s}/\mathrm{km}$). EDE cosmologies that can resolve the Hubble tension and fit the baseline dataset require an enhanced amplitude and slope near the pivot scale relative to $\mathrm{\Lambda }\mathrm{CDM}$ cosmologies. These requirements, particularly the steeper derivative, are in tension with the $\mathrm{Ly}\alpha$ measurements. This figure is for illustrative purposes and thus does not include errors for the $\mathrm{Ly}\alpha$ data.

Figure 2

Marginalized posteriors for a subset of EDE and $\mathrm{\Lambda }\mathrm{CDM}$ parameters with and without $\mathrm{Ly}\alpha$ data. The baseline dataset (gray) consists of Planck 2018 high-$\ell$ ($\mathrm{TT}+\mathrm{TE}+\mathrm{EE}$) and low-$\ell$ ($\mathrm{TT}+\mathrm{EE}$) measurements, as well as BOSS DR12, SDSS MGS, and 6dFGS BAO data. Including eBOSS $\mathrm{Ly}\alpha$ data (blue) or XQ-100 $\mathrm{Ly}\alpha$ data (red) significantly reduces the upper bound on $f_{\mathrm{EDE}}$. $H_0$ values that are able to resolve the Hubble tension are strongly excluded by both analyses that include $\mathrm{Ly}\alpha$ data. The top right panel shows constraints in the ${\mathrm{\Delta }}_L^2\text{−}{n}_L$ plane for each of these datasets, and the $\mathrm{Ly}\alpha$ likelihoods alone (dashed lines). Although both $\mathrm{Ly}\alpha$ likelihoods are in significant tension with the baseline analysis, our conclusions are unchanged even if we artificially shift the center of the eBOSS $\mathrm{Ly}\alpha$ likelihood to the posterior mean of the baseline $\mathrm{\Lambda }\mathrm{CDM}$ analysis (orange).