Nonlinear stability of cosmological solutions in massive gravity
Abstract
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Keywords
Cite
@article{arxiv.1303.4154,
title = {Nonlinear stability of cosmological solutions in massive gravity},
author = {Antonio De Felice and A. Emir Gumrukcuoglu and Chunshan Lin and Shinji Mukohyama},
journal= {arXiv preprint arXiv:1303.4154},
year = {2013}
}
Comments
28 pages ; v2. Minor changes to match the published version