  Conformal relativity theory which is also known as Hoyle-Narlikar theory has
recently been given some new interest. It is an extended relativity theory
which is invariant with respect to conformal transformations of the metric.
  In this paper we show how conformal relativity is related to the Brans-Dicke
theory and to the low-energy-effective superstring theory. We show that
conformal relativity action is equaivalent to a transformed Brans-Dicke action
for Brans-Dicke parameter $\omega = -3/2$ in contrast to a reduced
(graviton-dilaton) low-energy-effective superstring action which corresponds to
a Brans-Dicke action with Brans-Dicke parameter $\omega = -1$. In fact,
Brans-Dicke parameter $\omega =-3/2$ gives a border between a standard scalar
field evolution and a ghost.
  We also present basic cosmological solutions of conformal relativity in both
Einstein and string frames. The Eintein limit for flat conformal cosmology
solutions is unique and it is flat Minkowski space. This requires the scalar
field/mass evolution instead of the scale factor evolution in order to explain
cosmological redshift.
  It is interesting that like in ekpyrotic/cyclic models, a possible transition
through a singularity in conformal cosmology in the string frame takes place in
the weak coupling regime.
