Cosmological Solutions of the Non-minimally Coupled Weyl Connection Gravity Theories

TL;DR

This paper explores a non-minimally coupled Weyl connection gravity model, demonstrating that it admits cosmological solutions with fine-tuned curvature, potentially offering a viable framework for describing the universe's large-scale structure.

Contribution

It introduces a novel non-minimally coupled Weyl connection gravity model and shows it can produce cosmological solutions with adjustable curvature.

Findings

Solutions in space-form with small reference curvature

Model can be fine-tuned to match vacuum energy contributions

Potential for a workable cosmological description

Abstract

We consider a non-minimally coupled curvature-matter gravity model (NMC) with a Weyl connection, a theory referred to as non-minimally coupled Weyl connection gravity (NMCWCG). The Weyl connection is an affine connection that is not compatible with the metric, and involves a vector field. Assuming a vacuum expectation value for the vector field and a matter Lagrangian that only contains the contributions of the vacuum energy, we show that the model admits solutions in the space-form with a reference curvature that can be fine-tuned to much smaller values than the contribution of the matter fields. This shows that, at least in principle, the model admits a workable cosmological description.