Effective field equations and scale-dependent couplings in gravity

TL;DR

This paper introduces a comprehensive set of scale-dependent gravitational field equations incorporating variable G and Lambda, and explores their cosmological implications within the Asymptotic Safety framework, revealing diverse cosmic evolution scenarios.

Contribution

It presents the most general consistent equations for gravity with scale-dependent couplings, extending Einstein's equations with new kinetic and derivative terms, and applies them to early universe cosmology.

Findings

Discovery of bouncing and recollapsing solutions

Identification of non-singular expanding universes with transient acceleration

Demonstration of diverse cosmological evolutions under scale-dependent gravity

Abstract

A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $\Lambda(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent, physically plausible, set of evolution equations assuming at most second derivatives in the dynamical variables. In the new Einstein's equations, only $\Lambda$-kinetic terms arise, while in the modified conservation equation, derivative terms of $G$ also appear. As an application, this formalism is applied in the context of the Asymptotic Safety scenario to the early universe, assuming a perfect fluid with a radiation equation of state. Cosmological solutions are obtained for all types of spatial curvature, displaying a variety of interesting cosmic evolutions. As an indication of such behaviours, bouncing solutions, recollapsing solutions or non-singular expanding solutions with a transient acceleration era are discussed in details.