Constraining Early Dark Energy with Large-Scale Structure

TL;DR

The paper tests Early Dark Energy (EDE) as a fix for the Hubble tension by integrating the EFT of Large-Scale Structure with the full-shape BOSS FS+BAO data, varying the EDE triplet $(f_{ m EDE}, z_c, \theta_i)$ (with $n$ fixed, often $n=3$). It finds no evidence for EDE: Planck 2018 plus BOSS FS+BAO constrain $f_{ m EDE}<0.072$ (95% CL) and yield $H_0\approx 68.5$ km s$^{-1}$ Mpc$^{-1}$; including $S_8$ priors from DES-Y1, KV-450, and HSC tightens the bound to $f_{ m EDE}<0.053$ and shifts $H_0$ to $\approx 68.7$ km s$^{-1}$ Mpc$^{-1}$, with SH0ES remaining in tension. The analysis shows EFT-based BOSS constraints are significantly stronger than standard BAO/$f\sigma_8$-only approaches, and that future Euclid/DESI-like surveys can push the limit to $f_{ m EDE}<\mathcal{O}(10^{-2})$, potentially ruling out EDE as a solution. Together, these results argue against EDE as a viable resolution to the Hubble tension and highlight the power of EFT-LSS as a probe of beyond-$\Lambda$CDM physics in upcoming surveys.

Abstract

An axion-like field comprising $\sim 10\%$ 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. (2020), 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 $H_0$ compared to primary CMB data alone, yielding $H_0 = 68.54^{+0.52}_{-0.95}$ km/s/Mpc ($68\%$ CL). In addition, we constrain the maximum fractional energy density contribution of the EDE to $f_{\rm EDE} < 0.072$ ($95\%$ CL). 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 $H_0 = 68.73^{+0.42}_{-0.69}$ km/s/Mpc ($68\%$ CL) and $f_{\rm EDE}<0.053$ ($95\%$ CL). These bounds are obtained without including local-universe $H_0$ data, which is in strong tension with the CMB and LSS, even in the EDE model. We also refute claims that MCMC analyses of EDE that omit SH0ES from the combined dataset yield misleading posteriors. Finally, we demonstrate that upcoming Euclid/DESI-like spectroscopic galaxy surveys can 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.

Figures (13)

• Figure 1: Fraction of the cosmic energy density in the EDE field as a function of redshift, for the parameters in Eq. \ref{['hillparams']}.
• Figure 2: CMB TT (left panel), EE (middle panel), and TE (right panel) power spectra for $\Lambda$CDM (black, solid) and EDE (red, dashed), with $H_0 = 68.07$ km/s/Mpc and $H_0 = 71.15$ km/s/Mpc, respectively, and fractional difference between EDE and $\Lambda$CDM (bottom). The fractional difference for TT and EE is normalized to the $\Lambda$CDM spectra, while TE has been normalized by the variance to accommodate the zero crossings in this spectrum. The model parameters are given in Eqs. \ref{['hillparams']} and \ref{['hillparamsLCDM']} for EDE and $\Lambda$CDM, respectively, corresponding to the best-fit parameters from Hill:2020osr in the fit to primary CMB, CMB lensing, BAO, RSD, SNIa, and SH0ES data.
• Figure 3: Multipoles of the galaxy power spectra at $z=0.61$, before (left panel) and after (right panel) marginalizing over nuisance parameters, along with the high-$z$ NGC BOSS data. The predictions of the $\Lambda$CDM model are shown with solid curves, while the the EDE predictions are shown with dashed curves. In the right panel (after marginalizing over nuisance parameters) the curves cannot be distinguished by eye; the fractional difference in these curves is shown in Fig. \ref{['fig:multipoles']}.
• Figure 4: Multipoles of the galaxy power spectrum at $z=0.61$, after marginalizing over nuisance parameters as in the right panel of Fig. \ref{['fig:spectra']}. Left panel: Fractional difference between $\Lambda$CDM and EDE: $\Delta P/P\equiv(P^{\rm EDE}- P^{\Lambda{\rm CDM}})/P^{\Lambda{\rm CDM}}$. The monopole features a $0.3\%$ pattern produced by the mismatch in the shape of the BAO wiggles between the two models, whereas the quadrupole exhibits a $\mathcal{O}(2\%)$ fractional difference at low $k$. Right panel: Fractional difference in units of the BOSS data error bar for every wavenumber bin: $\Delta P/\sigma_P$. (Note that the neighboring $k$ bins are correlated). The biggest discrepancy is observed in the shape and position of the BAO wiggles in the monopole; see the main text for details.
• Figure 5: Posterior distributions for the parameters extracted from the joint Planck 2018 TT+TE+EE+low $\ell$+lensing + BOSS DR 12 (FS+BAO) likelihood. For reference, we also display the constraints from the Planck 2018 primary CMB data alone (TT+TE+EE), obtained in Hill:2020osr. The dark-shaded and light-shaded contours mark $68\%$ and $95\%$ confidence regions, respectively. The gray band shows the $H_0$ measurement from SH0ES, for comparison ($1\sigma$ and $2\sigma$ regions in dark and light gray, respectively).