Stable and unstable cosmological models in bimetric massive gravity
Abstract
Nonlinear, ghostfree massive gravity has two tensor fields; when both are dynamical, the mass of the graviton can lead to cosmic acceleration that agrees with background data, even in the absence of a cosmological constant. Here the question of the stability of linear perturbations in this bimetric theory is examined. Instabilities are presented for several classes of models, and simple criteria for the cosmological stability of massive bigravity are derived. In this way, we identify a particular selfaccelerating bigravity model, infinitebranch bigravity (IBB), which exhibits both viable background evolution and stable linear perturbations. We discuss the modified gravity parameters for IBB, which do not reduce to the standard Λ CDM result at early times, and compute the combined likelihood from measured growth data and type Ia supernovae. IBB predicts a present matter density Ω_{m 0}=0.18 and an equation of state w (z )=0.79 +0.21 z /(1 +z ) . The growth rate of structure is well approximated at late times by f (z )≈Ω_{m}^{0.47}[1 +0.21 z /(1 +z )] . The implications of the linear instability for other bigravity models are discussed: the instability does not necessarily rule these models out, but rather presents interesting questions about how to extract observables from them when linear perturbation theory does not hold.
 Publication:

Physical Review D
 Pub Date:
 December 2014
 DOI:
 10.1103/PhysRevD.90.124014
 arXiv:
 arXiv:1407.4331
 Bibcode:
 2014PhRvD..90l4014K
 Keywords:

 04.50.Kd;
 95.36.+x;
 98.80.k;
 Modified theories of gravity;
 Dark energy;
 Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 17 pages, 5 figures, version published in PRD