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Entropy 2012, 14(10), 1978-1996; doi:10.3390/e14101978

Conformal Relativity versus Brans–Dicke and Superstring Theories

 and 3,4,*
1 Institute for Theoretical Physics, University of Wrocław, 50-204 Wrocław, Poland 2 Bogoliubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia 3 Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland 4 Copernicus Center for Interdisciplinary Studies, Sławkowska 17, 31-016 Kraków, Poland
* Author to whom correspondence should be addressed.
Received: 20 August 2012 / Revised: 23 September 2012 / Accepted: 27 September 2012 / Published: 18 October 2012
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)
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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 ω = -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 ω = -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.
Keywords: conformal relativity; Brans–Dicke theory; superstring theory conformal relativity; Brans–Dicke theory; superstring theory
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Blaschke, D.B.; Dąbrowski, M.P. Conformal Relativity versus Brans–Dicke and Superstring Theories. Entropy 2012, 14, 1978-1996.

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