[Paper Review] Dissecting the $H_0$ and $S_8$ tensions with Planck + BAO + supernova type Ia in multi-parameter cosmologies

Luis A. Anchordoqui, Eleonora Di Valentino+2 more|arXiv (Cornell University)|Jul 29, 2021

Cosmology and Gravitation Theories214 references84 citations

TL;DR

This study investigates whether combined early- and late-time modifications to cosmological models can simultaneously resolve the H₀ and S₈ tensions using Planck CMB, BAO, and Type Ia supernova data. Despite exploring 24 multi-parameter models—including interacting dark energy, curved spacetime, and early-universe modifications—no viable configuration achieves a simultaneous solution to both tensions, indicating persistent incompatibility with the standard ΛCDM framework.

ABSTRACT

The mismatch between the locally measured expansion rate of the universe and the one inferred from observations of the cosmic microwave background (CMB) assuming the canonical $\Lambda$CDM model has become the new cornerstone of modern cosmology, and many new-physics set ups are rising to the challenge. Concomitant with the so-called $H_0$ problem, there is evidence of a growing tension between the CMB-preferred value and the local determination of the weighted amplitude of matter fluctuations $S_8$. It would be appealing and compelling if both the $H_0$ and $S_8$ tensions were resolved at once, but as yet none of the proposed new-physics models have done so to a satisfactory degree. Herein, we adopt a systematic approach to investigate the possible interconnection among the free parameters in several classes of models that typify the main theoretical frameworks tackling the tensions on the universe expansion rate and the clustering of matter. Our calculations are carried out using the publicly available Boltzmann solver CAMB in combination with the sampler CosmoMC. We show that even after combining the leading classes of models sampling modifications of both the early and late time universe a simultaneous solution to the $H_0$ and $S_8$ tensions remains elusive.

Motivation & Objective

• To assess whether combined early- and late-time modifications to cosmological models can resolve both the H₀ and S₈ tensions simultaneously.
• To systematically explore 24 combinations of models across early- and late-time physics, including interacting dark energy and curved spacetime.
• To evaluate the viability of multi-parameter extensions to ΛCDM in reconciling local H₀ measurements with CMB-inferred values.
• To investigate parameter degeneracies and cross-correlations that may hinder simultaneous tension resolution.
• To determine whether any model class provides a statistically consistent solution to both tensions within current observational constraints.

Proposed method

• Employs the Boltzmann solver CAMB and the CosmoMC sampling tool to compute cosmological observables and explore parameter space.
• Combines Planck 2018 CMB temperature and polarization data with Baryon Acoustic Oscillations (BAO) and Type Ia supernova (Pantheon) data.
• Explores 24 model combinations involving early-universe modifications (e.g., varying sound speed, early dark energy) and late-time modifications (e.g., interacting dark energy, curvature).
• Imposes standard priors on cosmological parameters and uses Bayesian evidence to assess model viability.
• Analyzes parameter cross-correlations and degeneracies to understand constraints and tensions in multi-dimensional parameter space.
• Uses the S₈ = σ₈√Ωₘ/0.3 statistic to quantify the amplitude of matter fluctuations tension.

Experimental results

Research questions

• RQ1 Can a simultaneous resolution of the H₀ and S₈ tensions be achieved through combined early- and late-time modifications to the ΛCDM model?
• RQ2 Which combinations of early- and late-time physics yield the most viable parameter space for resolving both tensions?
• RQ3 How do parameter degeneracies and cross-correlations affect the ability to resolve both tensions simultaneously?
• RQ4 Do interacting dark energy or curved spacetime models offer a more consistent solution than isolated modifications?
• RQ5 Is there any multi-parameter model that achieves a statistically acceptable fit to Planck, BAO, and supernova data while resolving both tensions?

Key findings

• No viable combination of early- and late-time modifications to ΛCDM simultaneously resolves both the H₀ and S₈ tensions within current observational constraints.
• Even with 24 explored model combinations, including interacting dark energy and curved spacetime, no model achieves a consistent solution to both tensions.
• The H₀ tension (4.2σ discrepancy between local and CMB-inferred values) and S₈ tension (3.4σ with BOSS+KV450) remain unresolved in all tested multi-parameter extensions.
• Parameter cross-correlations and degeneracies prevent effective cancellation of tensions across both observables.
• Models that reduce the sound horizon to alleviate H₀ tension tend to exacerbate the S₈ tension, and vice versa.
• The study concludes that resolving both tensions simultaneously remains elusive, suggesting a potential breakdown of the ΛCDM framework or the need for more radical physics.