Conformal Relativity versus Brans-Dicke and Superstring Theories

We show how conformal relativity is related to Brans-Dicke theory and to low-energy-effective superstring theory. Conformal relativity or the Hoyle-Narlikar theory is invariant with respect to conformal transformations of the metric. We show that the conformal relativity action is equivalent to the transformed Brans-Dicke action for omega = -3/2 (which is the border between standard scalar field and ghost) in contrast to the reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to the Brans-Dicke action with omega = -1. We show that like in ekpyrotic/cyclic models, the transition through the singularity in conformal cosmology in the string frame takes place in the weak coupling regime. We also find interesting self-duality and duality relations for the graviton-dilaton actions.