# Conformal Gravity and Transformations in the Symmetric Teleparallel Framework

## TL;DR

This paper explores conformal theories of gravity within the Symmetric Teleparallel framework, introducing scalar fields and analyzing their potential to explain dark energy through second-order field equations.

## Contribution

It constructs conformal gravity theories in the Symmetric Teleparallel setting with second-order equations and compares scalar-tensor formulations to Teleparallel Gravity.

## Key findings

- Existence of conformal theories with second-order equations
- Scalar-tensor representations of modified theories
- Potential dark energy role in a specific sub-case

## Abstract

Conformal symmetries appear in many parts of physics and play a unique role in exploring the Universe. In this work, we consider the possibility of constructing conformal theories of gravity in the Symmetric Teleparallel Gravity framework, where gravitation is expressed through non-metricity rather than curvature or torsion. We demonstrate that it is possible to formulate a family of conformal theories with second-order field equations and have the metric tensor as the fundamental variable. Moreover, we consider the addition of a scalar field to the theory, and compare the results to the Teleparallel Gravity setting. Finally, we present the scalar-tensor representation of modified symmetric teleparallel theories, and amongst others, we show that there is an interesting sub-case that has the possibility of playing the role of dark energy.