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Conformal symmetries appear in many parts of physics and play a unique rolein exploring the Universe. In this work, we consider the possibility ofconstructing conformal theories of gravity in the Symmetric TeleparallelGravity framework, where gravitation is expressed through non-metricity ratherthan curvature or torsion. We demonstrate that it is possible to formulate afamily of conformal theories with second-order field equations and have themetric tensor as the fundamental variable. Moreover, we consider the additionof a scalar field to the theory, and compare the results to the TeleparallelGravity setting. Finally, we present the scalar-tensor representation ofmodified symmetric teleparallel theories, and amongst others, we show thatthere is an interesting sub-case that has the possibility of playing the roleof dark energy.

Conformal Gravity and Transformations in the Symmetric Teleparallel Framework