[Paper Review] The $H_0$ and $S_8$ tensions necessitate early and late time changes to $Λ$CDM

Steven J. Clark, Kyriakos Vattis+2 more|arXiv (Cornell University)|Oct 18, 2021

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes a combined Early Dark Energy (EDE) and Decaying Dark Matter (DDM) model to simultaneously resolve the $H_0$ and $S_8$ tensions in cosmology. By introducing EDE to increase the Hubble constant and DDM to suppress late-time structure growth, the model reduces both tensions to within 95% credible intervals, with a strong preference over $Λ$CDM via $\Delta\text{AIC} = -6.72$. The solution requires both early and late-time modifications to $Λ$CDM, indicating a need for complementary physics across cosmic time.

ABSTRACT

An only early or only late time alteration to $Λ$CDM has been inadequate at resolving both the $H_0$ and $S_8$ tensions simultaneously; however, a combination of early and late time alterations to $Λ$CDM can provide a solution to both tensions. As an illustration, we examine a combined Early Dark Energy - Decaying Dark Matter model. While early dark energy has the ability to resolve the $H_0$ tension, it leads to a discrepancy in $S_8$ measurements. We show that the addition of decaying dark matter helps resolve the $S_8$ discrepancy that would otherwise be enhanced in an early dark energy model, while the latter is able to relieve the $H_0$ disagreement to within the 95th percentile interval. Our results show a preference for the combined model over $Λ$CDM with $Δ m{AIC} = -6.72$, hinting that both early and late universe modifications may be necessary to address the cosmological tensions.

Motivation & Objective

• To address the persistent $H_0$ and $S_8$ tensions in cosmology, which challenge the standard $\Lambda$CDM model.
• To investigate whether a combined early and late-time modification to $\Lambda$CDM can simultaneously resolve both tensions.
• To test the viability of a model combining Early Dark Energy (EDE) and Decaying Dark Matter (DDM) as a unified solution.
• To evaluate the statistical preference of the EDE-DDM model over standard $\Lambda$CDM using information criteria like AIC.
• To explore the degeneracy structure and prior sensitivity of DDM parameters in the context of current cosmological data.

Proposed method

• The study employs a modified $\Lambda$CDM framework with an additional early dark energy component that becomes dominant at high redshift ($z \gtrsim 3000$), reducing the sound horizon and increasing $H_0$.
• A decaying dark matter component is introduced, where a massive cold dark matter particle decays into a massless and a massive daughter particle ($\psi \to \gamma' + \chi$), suppressing late-time structure formation.
• Cosmological parameter estimation is performed using Markov Chain Monte Carlo (MCMC) sampling with both linear and logarithmic priors on DDM parameters to assess prior sensitivity.
• The model is tested against multiple datasets, including CMB anisotropy power spectra, BAO measurements, and late-time $H_0$ and $S_8$ observations.
• Model comparison is conducted using the Akaike Information Criterion (AIC), with $\Delta\text{AIC}$ used to quantify the preference for the EDE-DDM model over $\Lambda$CDM.
• The analysis evaluates posterior distributions of key parameters, including $\Omega_{\text{EDE}}$, $a_{\text{EDE}}$, $\Gamma$, and $\epsilon$, to assess their constraints and degeneracies.

Experimental results

Research questions

• RQ1 Can a combined early and late-time modification to $\Lambda$CDM simultaneously resolve both the $H_0$ and $S_8$ tensions?
• RQ2 Does the inclusion of decaying dark matter mitigate the $S_8$ enhancement caused by early dark energy in the EDE model?
• RQ3 How does the statistical preference of the EDE-DDM model compare to $\Lambda$CDM, as quantified by information criteria?
• RQ4 What are the constraints on the EDE and DDM parameters, and how do they depend on prior assumptions such as linear vs. logarithmic priors?
• RQ5 To what extent do the DDM parameters $\Gamma$ and $\epsilon$ influence the $S_8$ value, and can they restore consistency with late-time measurements?

Key findings

• The combined EDE-DDM model reduces the $H_0$ tension to $1.6\sigma$ with $H_0 = 71 \pm 1 \, \text{km} \, \text{s}^{-1} \, \text{Mpc}^{-1}$, bringing it within the 95th percentile interval.
• The $S_8$ tension is fully resolved, with $S_8 = 0.78 \pm 0.02$, reducing the discrepancy to $0.4\sigma$ from late-time measurements.
• The model shows a strong statistical preference over $\Lambda$CDM, with $\Delta\text{AIC} = -6.72$, indicating improved fit despite additional parameters.
• The EDE component is constrained to $\Omega_{\text{EDE}} = 2.1_{-0.9}^{+0.8} \times 10^{-7}$ and $\log_{10}(a_{\text{EDE}}) = -3.69_{-0.08}^{+0.06}$, consistent with previous EDE studies.
• The DDM parameters are constrained to $\Gamma < 0.017 \, \text{Gyr}^{-1}$ and $\epsilon < 0.016$, with posteriors consistent with zero but still effective in suppressing $S_8$.
• The posterior distributions of $\Gamma$ and $\epsilon$ are degenerate with $\Lambda$CDM, but their inclusion decouples $S_8$ from $\Omega_{\text{cdm}}^{\text{ini}}$, enabling consistency with late-time data.