Perturbations in massive gravity cosmology

• Published in: The journal of high energy physics Vol. 2012; no. 6
• Main Authors: Comelli, D., Crisostomi, M., Pilo, L.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2012; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Cosmology; Dark matter; Degrees of freedom; Elementary Particles; Gravitation; Gravity; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; Scalars; String Theory; Tensors; Classical Theories of Gravity; Cosmology of Theories beyond the SM
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2012)085

A bstract We study cosmological perturbations for a ghost free massive gravity theory formulated with a dynamical extra metric that is needed to massive deform GR. In this formulation FRW background solutions fall in two branches. In the dynamics of perturbations around the first branch solutions, no extra degree of freedom with respect to GR is present at linearized level, likewise what is found in the Stuckelberg formulation of massive gravity where the extra metric is flat and non dynamical. In the first branch, perturbations are probably strongly coupled. On the contrary, for perturbations around the second branch solutions all expected degrees of freedom propagate. While tensor and vector perturbations of the physical metric that couples with matter follow closely the ones of GR, scalars develop an exponential Jeans-like instability on sub-horizon scales. On the other hand, around a de Sitter background there is no instability. We argue that one could get rid of the instabilities by introducing a mirror dark matter sector minimally coupled to only the second metric.