Scale-dependent gravity and covariant scale-setting

TL;DR

This paper introduces a covariant scale-setting method in scale-dependent gravity, leading to models that can avoid the Big Bang singularity or alleviate the Hubble tension, with implications for cosmological structure formation.

Contribution

It proposes a new covariant scale-setting expression and develops models of running gravitational and cosmological constants consistent with energy-momentum conservation.

Findings

One model avoids the Big Bang singularity.

Another model alleviates the Hubble tension.

Basic solutions for cosmological perturbations are derived.

Abstract

A fundamental element of scale-dependent gravity is the scale-setting procedure. We present a new covariant expression to set the scale that arises when examining the field equations. Considering the renormalization group equations and imposing energy-momentum tensor conservation, we arrive at two models of running of the gravitational and cosmological constants. In the cosmological setting, we found that in one model the Big Bang singularity is avoided, while in the other the Hubble tension can be alleviated. At the level of cosmological perturbations, we derived the basic solutions and qualitatively discussed the impacts of this scenario on structure formation.