Auxiliary fields representation for modified gravity models

Davi C. Rodrigues, Filipe de O. Salles, Ilya L. Shapiro, and Alexei A. Starobinsky
Phys. Rev. D 83, 084028 – Published 15 April 2011

Abstract

We consider tensor-multiscalar representations for several types of modified gravity actions. The first example is the theory with the action representing an arbitrary smooth function of the scalar curvature R and R, the integrand of the Gauss-Bonnet term and the square of the Weyl tensor. We present a simple procedure leading to an equivalent theory of a space-time metric and four auxiliary scalars and especially discuss the calibration of a cosmological constant and the condition of the existence of de Sitter-like solutions in the case of an empty universe. The condition for obtaining a smaller number of independent scalar fields is derived. The second example is the Eddington-like gravity action. In this case we show, in particular, the equivalence of the theory to general relativity with the cosmological constant term, with or without use of the first-order formalism, and also discuss some possible generalizations.

  • Received 21 January 2011

DOI:https://doi.org/10.1103/PhysRevD.83.084028

© 2011 American Physical Society

Authors & Affiliations

Davi C. Rodrigues*

  • Departamento de Física, CCE, Universidade Federal do Espírito Santo, 29075-910, Vitória, ES, Brazil

Filipe de O. Salles and Ilya L. Shapiro‡,§

  • Departamento de Física, ICE, Universidade Federal de Juiz de Fora, 36036-330, MG, Brazil

Alexei A. Starobinsky

  • Landau Institute for Theoretical Physics, Moscow, 119334, Russia; RESCEU, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan

  • *davirodrigues.ufes@gmail.com
  • salles@ice.ufjf.br
  • shapiro@fisica.ufjf.br
  • §Also at Tomsk State Pedagogical University, Tomsk, Russia
  • alstar@landau.ac.ru

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Issue

Vol. 83, Iss. 8 — 15 April 2011

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