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Conformal Relativity versus Brans–Dicke and Superstring Theories
Institute for Theoretical Physics, University of Wrocław, 50-204 Wrocław, Poland
Bogoliubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
Copernicus Center for Interdisciplinary Studies, Sławkowska 17, 31-016 Kraków, Poland
* Author to whom correspondence should be addressed.
Received: 20 August 2012; in revised form: 23 September 2012 / Accepted: 27 September 2012 / Published: 18 October 2012
Abstract: 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
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Blaschke, D.B.; Dąbrowski, M.P. Conformal Relativity versus Brans–Dicke and Superstring Theories. Entropy 2012, 14, 1978-1996.
Blaschke DB, Dąbrowski MP. Conformal Relativity versus Brans–Dicke and Superstring Theories. Entropy. 2012; 14(10):1978-1996.
Blaschke, David B.; Dąbrowski, Mariusz P. 2012. "Conformal Relativity versus Brans–Dicke and Superstring Theories." Entropy 14, no. 10: 1978-1996.