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

Conformal Relativity versus Brans–Dicke and Superstring Theories

1,2
 and
3,4,*
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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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 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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