Conformal relativity versus Brans-Dicke and superstring theories
  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. 
David Blaschke and Mariusz P. Dabrowski