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Inflation and the conformal structure of higher-order gravity theories

Authors
Journal
Physics Letters B
0370-2693
Publisher
Elsevier
Publication Date
Volume
214
Issue
4
Identifiers
DOI: 10.1016/0370-2693(88)90110-4
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract We examine gravity theories derived from a gravitational lagrangian that is and analytic function ƒ(R) of the scalar curvature R in a space-time of arbitrary dimension D. We show that they are conformally equivalent to general relativity plus a scalar-field matter source with a particular self-interaction potential. The general form of this potential is calculated to be V(ø) = 1 2[Rƒ′(R)−ƒ(R)][ƒ′(R)] D (2−D) , where exp (ø) = [ƒ′ (R)] 2 (D−2) . Flat potentials arise as ø→+∞ for polynomial lagrangians of leading order β whenever D = 2 β. Several explicit examples are given and discussed with reference to inflation. We show how our results can lead to singularity theorems for gravity theories derived from a general lagrangian.

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