[Paper Review] Thermal Friction as a Solution to the Hubble and Large-Scale Structure Tensions

Kim V. Berghaus, Tanvi Karwal|arXiv (Cornell University)|Apr 19, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes thermal friction on a scalar field in the early universe as a solution to the Hubble and large-scale structure tensions, where energy is transferred to dark radiation, mimicking early dark energy (EDE) and extra radiation. The model performs best when energy transfer occurs at very high redshifts (z ≳ 10⁵), asymptoting to an extra self-interacting radiation species, which alleviates both tensions but does not fully resolve them due to CMB incompatibility with late-time perturbations.

ABSTRACT

Thermal friction offers a promising solution to the Hubble and the large-scale structure (LSS) tensions. This additional friction acts on a scalar field in the early universe and extracts its energy density into dark radiation, the cumulative effect being similar to that of an early dark energy (EDE) scenario. The dark radiation automatically redshifts at the minimal necessary rate to improve the Hubble tension. On the other hand, the addition of extra radiation to the Universe can improve the LSS tension. We explore this model in light of cosmic microwave background (CMB), baryon acoustic oscillation and supernova data, including the SH0ES $H_0$ measurement and the Dark Energy Survey Y1 data release in our analysis. Our results indicate a preference for the regime where the scalar field converts to dark radiation at very high redshifts, asymptoting effectively to an extra self-interacting radiation species rather than an EDE-like injection. In this limit, thermal friction can ease both the Hubble and the LSS tensions, but not resolve them. We find the source of this preference to be the incompatibility of the CMB data with the linear density perturbations of the dark radiation when injected at redshifts close to matter-radiation equality.

Motivation & Objective

• To address the Hubble tension (discrepancy in H₀ measurements) and the large-scale structure tension (σ₈ discrepancy) within a single physical framework.
• To explore whether thermal friction on a scalar field can simultaneously ease both cosmological tensions by generating dark radiation.
• To test the viability of this model against CMB, BAO, type Ia supernova, SH0ES, and DES Y1 data.
• To determine the preferred redshift for energy transfer and assess whether the model behaves like EDE or extra radiation in the high-redshift limit.
• To investigate the origin of model preference and the role of dark radiation perturbations in fitting CMB data.

Proposed method

• Modeling a scalar field with thermal friction (Γ) that extracts energy into dark radiation, with the dark radiation redshifting at the minimal rate needed for EDE-like behavior.
• Deriving perturbation equations and initial conditions in synchronous gauge to compute cosmic microwave background (CMB) anisotropies and large-scale structure growth.
• Fitting the model to multiple datasets: CMB (Planck), BAO, type Ia supernovae, SH0ES H₀ measurement, and DES Y1 weak lensing data.
• Using Markov Chain Monte Carlo (MCMC) sampling with hierarchical priors to constrain parameters including Γ, initial scalar field value φᵢ, and effective number of neutrino species Nₑff.
• Comparing model performance using ΔBIC and χ² statistics to assess whether thermal friction improves fit over ΛCDM and EDE models.
• Analyzing the redshift dependence of energy injection and its impact on the evolution of density perturbations in dark radiation.

Experimental results

Research questions

• RQ1 Can thermal friction on a scalar field simultaneously alleviate the Hubble and large-scale structure tensions without requiring fine-tuned potentials?
• RQ2 At what redshift does energy transfer from the scalar field to dark radiation become most favored by cosmological data?
• RQ3 Does the model behave more like early dark energy (EDE) or extra radiation (Nₑff) in the high-redshift limit?
• RQ4 Why is the model disfavored when energy injection occurs near matter-radiation equality, and how does this relate to CMB data?
• RQ5 Can the inclusion of DES Y1 data and SH0ES H₀ measurement improve constraints on the thermal friction model?

Key findings

• The model performs best when the scalar field transfers energy to dark radiation at very high redshifts (z ≳ 10⁵), where it asymptotically behaves like an extra self-interacting radiation species.
• The preferred regime avoids the EDE-like injection profile and instead mimics a stable, self-interacting radiation component, improving fit to CMB and BAO data.
• The model reduces the Hubble tension but does not fully resolve it, with best-fit H₀ values around 68.9–71.1 km/s/Mpc depending on dataset combination.
• The CMB data disfavor energy injection near matter-radiation equality due to incompatibility with linear dark radiation perturbations, explaining the high-redshift preference.
• Including SH0ES and DES Y1 data improves constraints, with ΔBIC favoring the thermal friction model over ΛCDM when SH0ES is included, though not decisively.
• The model shows no significant improvement over ΛCDM + Nₑff in some cases, but the thermal friction mechanism provides a dynamical origin for extra radiation without fine-tuning.