# Nonminimally coupled Weyl gravity

## TL;DR

This paper explores Weyl gravity with a non-minimal matter-curvature coupling, revealing properties from non-metricity that lead to a second order theory compatible with a cosmological constant under specific conditions.

## Contribution

It introduces a novel non-minimal coupling in Weyl gravity and analyzes its implications for the theory's properties and vacuum solutions.

## Key findings

- Vacuum solutions compatible with a cosmological constant
- Properties arising from non-metricity in the theory
- Conditions on the vector field for compatibility

## Abstract

Weyl gravity in the presence of a non-minimal matter-curvature coupling is presented. Some properties arising from the non-metricity give rise to a second order theory whose vacuum is compatible with a cosmological constant, under conditions on the vector field.