Reconstruction of A Scale-Dependent Gravitational Phase Transition

TL;DR

This paper extends a gravitational phase transition model to include scale-dependent modifications in Einstein equations, analyzing data to test deviations from general relativity and addressing tensions in cosmological measurements.

Contribution

It introduces a scale-dependent extension to the gravitational phase transition model and demonstrates its ability to reconcile conflicting cosmological datasets.

Findings

No significant deviation from GR detected.

Reconciliation of H0 measurements from different datasets.

Reduction of σ8 tension to less than 1σ.

Abstract

In this work we extend our earlier phenomenological model for a gravitational phase transition (GPT) and its generalization to early times by letting the modifications in the linearly-perturbed Einstein equations be scale-dependent. These modifications are characterized as deviations of the parameters $\mu(z,k)$ and $\gamma(z,k)$ from their values in general relativity (GR). The scale-dependent amplitudes of modified $\mu(z,k)$ and $\gamma(z,k)$ and the parameters defining the phase transition, along with the standard cosmological parameters, are measured by various data combinations. Out of the perturbation parameters, we construct gravity eigenmodes which represent patterns of perturbations best detectable by data. We detect no significant deviation from GR in these parameters. However, the larger parameter space produced due to the new degrees of freedom allows for the reconciliation of various datasets which are in tension in $\Lambda$CDM. In particular, we find $H_0=71.9\pm 9.2$ from anisotropies of the Cosmic Microwave Background as measured by Planck and various measurements of the Baryonic Acoustic Oscillations, in agreement with local Hubble measurements. We also find that the $\sigma_8$ tension between the measurements of Dark Energy Survey and Planck is reduced to less than $1\sigma$.