Conformal transformations play a widespread role in gravity theories in
regard to their cosmological and other implications. In the pure metric theory
of gravity, conformal transformations change the frame to a new one wherein one
obtains a conformal-invariant scalar-tensor theory such that the scalar field,
deriving from the conformal factor, is a ghost.
In this work, conformal transformations ... [Show full abstract] and ghosts will be analyzed in the
framework of the metric-affine theory of gravity. Within this framework, metric
and connection are independent variables, and hence, transform independently
under conformal transformations. It will be shown that, if affine connection is
invariant under conformal transformations then the scalar field under concern
is a non-ghost, non-dynamical field. It is an auxiliary field at the classical
level, and might develop a kinetic term at the quantum level.
Alternatively, if connection transforms additively with a structure similar
to yet more general than that of the Levi-Civita connection, the resulting
action describes the gravitational dynamics correctly, and more importantly,
the scalar field becomes a dynamical non-ghost field. The equations of motion,
for generic geometrical and matter-sector variables, do not reduce connection
to the Levi-Civita connection, and hence, independence of connection from
metric is maintained. Therefore, metric-affine gravity provides an arena in
which ghosts arising from conformal factor are avoided thanks to the
independence of connection from the metric.