Stable cosmology in generalized massive gravity

Abstract

We present a thorough analysis of the cosmological perturbations in Generalised Massive Gravity. This is an extension of de Rham-Gabadadze-Tolley theory where the translation invariance in the Stückelberg field space is broken. This allows the mass parameters to be promoted to functions of the Stückelberg fields. We consider an exact cosmological background in this theory and study the stability of perturbations. We derive conditions to avoid ghost, gradient and tachyonic instability. The cosmology is an extension of the self-accelerating branch of the constant mass parameter theory, but now all five massive graviton polarisations propagate. For concreteness, we consider a minimal version of the theory where cosmology undergoes an accelerated expansion at late times and show that the perturbative stability is preserved for a range of parameters. 1 Approximately FLRW backgrounds may be safe against perturbations [10,11], although the lack of overall homogeneity and/or isotropy poses a technical challenge for obtaining accurate predictions beyond the background level. There also exist exact FLRW solutions that have a spatially isotropic fiducial metric [12,13] but these solutions are likely to be unstable [14].

Massive gravity with nonminimal coupling

“…This is compatible with what was found in the generalized dRGT without conformal transformation [22]. Finally, we calculate the sound speeds of the scalar degrees of freedom.…”

“…All of the expressions for this theory recovers the results of Ref. [22] in the limit G → 1 and _ ξ → ξð ffiffi ffi κ p r=a − HÞ (or equivalently, D → 0).…”

“…For solar system tests, we expect that the theory (35) exhibits Vainshtein mechanism due to its connection to generalized Galileon theories in the decoupling limit. The phenomenology of this theory will be investigated in a future publication [39]. Conversely, the theory (38) is disconnected from the dRGT construction, thus the existence and/or necessity of a screening mechanism needs to be confirmed.…”

“…In this theory called the generalized dRGT theory, the constant parameters in the graviton potential are promoted to be arbitrary functions of four auxiliary fields ϕ a , and the total number of physical degrees of freedom remains the same as the dRGT theory; i.e., the BD ghost is absent. Furthermore, it has been recently shown that all perturbations around the open-FLRW background are free from any instabilities [22]. Now, it is interesting to know how far we can generalize (global) Lorentz-invariant massive gravity theories.…”

Cosmic acceleration and growth of structure in massive gravity

“…The stability of these backgrounds was shown in some decoupling limit in Ref. [15] and later in a complete study of linear perturbations [17]. To our knowledge, this is the only massive gravity theory with 5 degrees of freedom that admits a stable FLRW solution and produces late time acceleration without any other source.…”