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arXiv · 1303.4154

Nonlinear stability of cosmological solutions in massive gravity

Antonio De Felice·A. Emir Gumrukcuoglu·Chunshan Lin·Shinji Mukohyama
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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.

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Antonio De Felice, A. Emir Gumrukcuoglu, Chunshan Lin, Shinji Mukohyama. 2013-06-04. Nonlinear stability of cosmological solutions in massive gravity. https://doi.org/10.1088/1475-7516%2F2013%2F05%2F035

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