Is Asymptotically Weyl-Invariant Gravity Viable?

TL;DR

This paper investigates a modified gravity theory called asymptotically Weyl-invariant gravity (AWIG), analyzing its cosmological dynamics and viability through phase space analysis, and finds it can reproduce key cosmic expansion phases without singularities.

Contribution

The study introduces and analyzes a simple implementation of AWIG, demonstrating its potential to model realistic cosmic evolution with accelerated and decelerated phases.

Findings

Model exhibits de Sitter, radiation, and matter-dominated fixed points.

Consistent with early and late accelerated expansion.

No obvious curvature singularities found.

Abstract

We explore the cosmological viability of a theory of gravity defined by the Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in the Palatini formalism, where $n\left(\mathcal{R}\right)$ is a dimensionless function of the Palatini scalar curvature $\mathcal{R}$ that interpolates between general relativity when $n\left(\mathcal{R}\right)=1$ and a locally scale-invariant and superficially renormalizable theory when $n\left(\mathcal{R}\right)=2$. We refer to this model as asymptotically Weyl-invariant gravity (AWIG). We analyse perhaps the simplest possible implementation of AWIG. A phase space analysis yields three fixed points with effective equation of states corresponding to de Sitter, radiation and matter-dominated phases. An analysis of the deceleration parameter suggests our model is consistent with an early and late period of accelerated cosmic expansion, with an intermediate period of decelerated expansion. We show that the model contains no obvious curvature singularities. Therefore, AWIG appears to be cosmologically viable, at least for the simple implementation explored.