Toward a simultaneous resolution of the $H_0$ and $S_8$ tensions: early dark energy and an interacting dark sector model

TL;DR

This work evaluates whether a joint model merging Early Dark Energy ($EDE$) with an interacting dark energy–dark matter sector ($iDEDM$) can simultaneously address the $H_0$ and $S_8$ tensions. $EDE$ reduces the sound horizon $r_s$ to raise $H_0$ but often increases $S_8$ via a higher early-time DM density, while $iDEDM$ suppresses small-scale growth by transferring energy from DE to DM, lowering $S_8$. Through MCMC analysis using Planck 2018, DESI BAO, DES, Pantheon+, and SH0ES data, the mixed model yields modest improvements in both tensions with $H_0 \approx 70.0$ km s$^{-1}$ Mpc$^{-1}$ and $S_8 \approx 0.815$, but remains short of a full resolution; the enhanced total matter density required by both components suppresses the effectiveness of $EDE$ in lowering the angular sound-horizon scale $\theta_s$. The $f_{ m EDE}$ and $\\xi$ parameters are bounded ($f_{ m EDE} < 0.113$, $\\xi < 0.071$, 95% CL), and the improvement over $\\Lambda$CDM is marginal once model complexity is penalized. The study highlights the challenge of jointly reconciling the two tensions and suggests that more flexible dark-sector models and upcoming high-precision surveys will be essential to thoroughly test such scenarios.

Abstract

The tension between the Hubble constant ($H_0$) inferred from the cosmic microwave background (CMB) and that measured from late-time observations, such as the local distance ladder, is a major challenge in modern cosmology. Early dark energy (EDE) has been proposed as a possible resolution to the $H_0$ tension, but it typically worsens the $S_8$ tension by enhancing the small-scale matter power spectrum due to an increased cold dark matter density. To address this issue, we propose a model that combines EDE with an interacting dark energy-dark matter (iDEDM) scenario, and investigate whether this mixed model can simultaneously resolve both tensions. We find that the DE-DM interaction suppress the growth of structure and reduce $S_8$, while EDE contributes to increase $H_0$, although less effectively than in the EDE-only case. Our MCMC analysis using Planck 2018, DESI BAO, DES, Pantheon+, and SH0ES data shows that the mixed model provides modest improvements in both tensions, although it does not fully resolve either. This limitation appears to stem from the fact that both EDE and iDEDM independently favor a higher present-day matter density, which reduces the angular diameter distance and limits the degree to which EDE can lower the sound horizon.

Figures (5)

• Figure 1: Non-linear matter power spectrum $P(k)$ at $z = 0$ for $\Lambda$CDM (dashed black line), EDE (solid red line) and iDEDM (solid blue line) models. We use the best-fit values from Ref. ede-smith for EDE and Ref. Lucca2021 for iDEDM.
• Figure 2: Cosmological parameter constraints from combined dataset of P18, DESI, DES, PP, and H0. The green, gray, red, and blue contours show $68\%$ and $95\%$ C.L. posteriors in the EDE-only, iDEDM-only, EDE-iDEDM (mixed), and $\Lambda$CDM models, respectively.
• Figure 3: Relative difference in the CMB temperature power spectrum with respect to $\Lambda$CDM, $(C_\ell - C_\ell^{\Lambda \mathrm{CDM}})/C_\ell^{\Lambda \mathrm{CDM}}$. The spectra are computed using the best-fit parameters from each model.
• Figure 4: Matter power spectrum $P(k)$ for the $\Lambda$CDM, EDE-only, iDEDM-only, and mixed models, computed at $z=0$ using best-fit parameters.
• Figure 5: Relative difference in the matter power spectrum with respect to $\Lambda$CDM, defined as $\Delta P/P \equiv (P - P_{\Lambda \mathrm{CDM}})/P_{\Lambda \mathrm{CDM}}$.