Exact Solution to the "Auxiliary Extra Dimension" Model of Massive Gravity

Abstract

The "Auxiliary Extra Dimension" model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.

v3:8 pages, LaTex, a comment and a reference added, version to appear in PLB

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• The Self-Accelerating Universe with Vectors in Massive Gravity
• Spatially Covariant Theories of a Transverse, Traceless Graviton, Part I: Formalism
• Emergent gravity from hidden sectors and TT deformations
• Generalized Framework for Auxiliary Extra Dimensions
• Cosmological constant constraints from observation-derived energy condition bounds and their application to bimetric massive gravity
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity