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Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aether

Radouane Gannouji1,2 and M. Sami3

  • 1Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
  • 2Institute of Theoretical Astrophysics, University of Oslo, 0315 Oslo, Norway
  • 3Centre of Theoretical Physics, Jamia Millia Islamia, New Delhi-110025, India

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Phys. Rev. D 85, 024019 – Published 13 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.024019

Abstract

We derive field equations of Gauss-Bonnet gravity in four dimensions after dimensional reduction of the action and demonstrate that in this scenario the Vainshtein mechanism operates in the flat spherically symmetric background. We show that inside this Vainshtein sphere the fifth force is negligibly small compared to the gravitational force. We also investigate the stability of the spherically symmetric solution, and clarify the vocabulary used in the literature about the hyperbolicity of the equation and the ghost-Laplacian stability conditions. We find superluminal behavior of the perturbation of the field in the radial direction. However, because of the presence of the nonlinear terms, the structure of the space-time is modified and as a result the field does not propagate in the Minkowski metric but rather in an “aether” composed of the scalar field π(r). We thereby demonstrate that the superluminal behavior does not create time paradoxes thanks to the absence of causal closed curves. We also derive the stability conditions for a Friedmann universe in context with scalar and tensor perturbations and we study the cosmology of the model.

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Phys. Rev. D 85, 024019– Published 13 January, 2012
  • Received 25 July 2011

© 2012 American Physical Society

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