Early Dark Energy Does Not Restore Cosmological Concordance

TL;DR

This work re-evaluates Early Dark Energy as a fix for the H0 tension by combining Planck 2018 CMB data with comprehensive LSS observations (DES-Y1, KV-450, HSC, KiDS), SNe data, and SH0ES. The analysis shows that while EDE can modestly raise H0 when SH0ES is included, its imprint on the matter power spectrum and growth leads to significant tension with LSS data; including DES-Y1 and other LSS priors largely removes evidence for EDE. When SH0ES is excluded, the data strongly favor ΛCDM with no need for EDE, reinforcing the difficulty of reconciling all datasets within EDE. Overall, the paper argues that EDE is unlikely to restore cosmological concordance and to resolve the H0 tension without creating new inconsistencies with LSS. The results underscore the power of cross-correlating CMB with LSS probes in testing early-universe modifications.

Abstract

Current cosmological data exhibit a tension between inferences of the Hubble constant, $H_0$, derived from early and late-universe measurements. One proposed solution is to introduce a new component in the early universe, which initially acts as "early dark energy" (EDE), thus decreasing the physical size of the sound horizon imprinted in the cosmic microwave background (CMB) and increasing the inferred $H_0$. Previous EDE analyses have shown this model can relax the $H_0$ tension, but the CMB-preferred value of the density fluctuation amplitude, $σ_8$, increases in EDE as compared to $Λ$CDM, increasing tension with large-scale structure (LSS) data. We show that the EDE model fit to CMB and SH0ES data yields scale-dependent changes in the matter power spectrum compared to $Λ$CDM, including $10\%$ more power at $k = 1~h$/Mpc. Motivated by this observation, we reanalyze the EDE scenario, considering LSS data in detail. We also update previous analyses by including $Planck$ 2018 CMB likelihoods, and perform the first search for EDE in $Planck$ data alone, which yields no evidence for EDE. We consider several data set combinations involving the primary CMB, CMB lensing, SNIa, BAO, RSD, weak lensing, galaxy clustering, and local distance-ladder data (SH0ES). While the EDE component is weakly detected (3$σ$) when including the SH0ES data and excluding most LSS data, this drops below 2$σ$ when further LSS data are included. Further, this result is in tension with strong constraints imposed on EDE by CMB and LSS data without SH0ES, which show no evidence for this model. We also show that physical priors on the fundamental scalar field parameters further weaken evidence for EDE. We conclude that the EDE scenario is, at best, no more likely to be concordant with all current cosmological data sets than $Λ$CDM, and appears unlikely to resolve the $H_0$ tension.

Figures (24)

• Figure 1: Constraints on the EDE scenario from Planck 2018 primary CMB data (TT+TE+EE); Planck 2018 CMB lensing data; BAO data from 6dF, SDSS DR7, and SDSS DR12; Pantheon SNIa data; the latest SH0ES $H_0$ constraint; SDSS DR12 RSD data; and the DES-Y1 3x2pt data. Here we present a subset of the parameters: the EDE energy-density fraction, timing, and initial condition, denoted $f_{\rm EDE}$, $\log_{10}(z_c)$, and $\theta_i$, respectively (note $\theta_i$ is distinct from $\theta_s$, the latter being the angular size of the sound horizon), along with $H_0$ [km/s/Mpc] and $\sigma_8$ . The contours show $1\sigma$ and $2\sigma$ posteriors for various data set combinations, computed with GetDistGetDist. The red contours show results for Planck primary CMB data alone; the blue contours additionally include Planck CMB lensing data, BAO data, SNIa data, SH0ES, and RSD data (matching the data sets used in Poulin:2018cxd and Smith:2019ihp, but with Planck 2018 replacing 2015); and the dark green contours further include the DES-Y1 3x2pt likelihood. The orange contours add priors on $S_8$ derived from KiDS and HSC data (as an approximation to the full likelihoods from these data sets). The Planck primary CMB data already place relatively strong constraints on the EDE scenario. Inclusion of the DES, KiDS, and HSC data significantly weakens the moderate evidence for EDE seen when analyzing the data sets used in Smith:2019ihp. The $H_0$ increase found in the EDE model fit in Smith:2019ihp (blue contours here) is noticeably reduced by the inclusion of LSS data, and the tension with SH0ES (shown in the gray bands) is no longer reconciled. The light green contours include all data sets except SH0ES, yielding a stringent upper bound $f_{\rm EDE} < 0.060$ at 95% CL, and a value for $H_0$ consistent with the fit to the primary CMB alone. Fig. \ref{['fig:no-SH0ES-logf-logm']} in Appendix \ref{['app:mfconstraints']} shows these constraints in terms of fundamental physics parameters.
• Figure 2: Fraction of the cosmic energy density in the EDE field $\phi$ as a function of redshift, for the parameters in Eq. \ref{['smithparams']}.
• Figure 3: CMB temperature anisotropy power spectra (left panel) and residuals (right panel) for $\Lambda$CDM (black, solid) and EDE (red, dashed) models, with $H_0 = 68.21$ km/s/Mpc and $H_0 = 72.19$ km/s/Mpc, respectively. The curves are nearly indistinguishable in the left panel. The model parameters are given by Eqs. \ref{['smithparams']} and \ref{['smithparamsLCDM']} for EDE and $\Lambda$CDM, respectively, corresponding to the Smith:2019ihp best-fit models to primary CMB, CMB lensing, BAO, RSD, SNIa, and SH0ES data.
• Figure 4: Non-linear matter power spectrum $P(k)$ at $z=0$ for $\Lambda$CDM and EDE models that fit the primary CMB, distances, and SH0ES data. The change in $\sigma_8$ in the EDE scenario can be seen as the relative increase in $P(k)$ in the range $0.1 \, h/{\rm Mpc} \lesssim k \lesssim 1 \, h/{\rm Mpc}$ (although $\sigma_8$ is computed from the linear rather than non-linear power spectrum). This increase is due primarily to shifts in the "standard" cosmological parameters in the EDE model, rather than the effects of the EDE itself. The model parameters are the same as in Fig. \ref{['fig:CMB_TT']} (see Eqs. \ref{['smithparams']} and \ref{['smithparamsLCDM']}).
• Figure 5: Ratio of the EDE and $\Lambda$CDM non-linear matter power spectra at $z$ values chosen to be the midpoints of the redshift bins used in the DES-Y1 analysis (and at $z=0$ in red). The model parameters are the same as in Fig. \ref{['fig:CMB_TT']}.