Conformal Gravity and Transformations in the Symmetric Teleparallel
  Framework
  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.
