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Gravitational Theories with Stable (anti-)de Sitter Backgrounds

  • Tirthabir BiswasEmail author
  • Alexey S. Koshelev
  • Anupam Mazumdar
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 183)

Abstract

In this article we will construct the most general torsion-free parity-invariant covariant theory of gravity that is free from ghost-like and tachyonic instabilities around constant curvature space-times in four dimensions. Specifically, this includes the Minkowski, de Sitter and anti-de Sitter backgrounds. We will first argue in details how starting from a general covariant action for the metric one arrives at an “equivalent” action that at most contains terms that are quadratic in curvatures but nevertheless is sufficient for the purpose of studying stability of the original action. We will then briefly discuss how such a “quadratic curvature action” can be decomposed in a covariant formalism into separate sectors involving the tensor, vector and scalar modes of the metric tensor; most of the details of the analysis however, will be presented in an accompanying paper. We will find that only the transverse and trace-less spin-2 graviton with its two helicity states and possibly a spin-0 Brans-Dicke type scalar degree of freedom are left to propagate in 4 dimensions. This will also enable us to arrive at the consistency conditions required to make the theory perturbatively stable around constant curvature backgrounds.

Keywords

Covariant Derivative Weyl Tensor Riemann Tensor Scalar Mode Equivalent Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We would like to thank Spyridon Talaganis for discussions. TB would like to thank Carl for his insightful comments on the general subject matter of IDG theories. AM is supported by the STFC grant ST/J000418/1. AK is supported by the FCT Portugal fellowship SFRH/BPD/105212/2014.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Tirthabir Biswas
    • 1
    Email author
  • Alexey S. Koshelev
    • 2
  • Anupam Mazumdar
    • 3
  1. 1.Loyola UniversityNew OrleansUSA
  2. 2.Departamento de Física and Centro de Matemática e AplicaçõesUniversidade da Beira InteriorCovilhãPortugal
  3. 3.Consortium for Fundamental PhysicsLancaster UniversityLancasterUK

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