Running Einstein Constant and a Possible Vacuum State of the Universe

TL;DR

This paper introduces a modified version of General Relativity where the Einstein constant varies with energy density, providing a phenomenological approach to dark energy and addressing the vacuum energy problem and Hubble tension.

Contribution

It proposes a variable Einstein constant framework, extending the theory via Taylor expansion, and explores its implications for dark energy and the Hubble tension.

Findings

Current vacuum energy value is consistent with zero within 1σ.

Modified model introduces a Chaplygin-like dark energy component.

Late-time Hubble parameter corrections align with observational data.

Abstract

We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of providing an effective dark energy density expression. Assuming a state close to vacuum, here defined by the vanishing product of the Einstein coupling constant and the Universe's energy density, we perform a Taylor expansion of the theory and hence extend it to the whole domain. In this framework, the (renormalized) vacuum energy problem is studied, and an additional constant pressure term, which induces a Chaplygin-like contribution to the dark energy sector, arises in the late-time dynamics. The correction to the late-time Hubble parameter is investigated by comparing theoretical predictions with the late Universe observational data. Our findings indicate that the current value of the stated vacuum energy is consistent with zero within 1$\sigma$. Implications of the modified $\Lambda$CDM model with respect to the Hubble tension are also discussed.