A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

Abstract

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.

Effective field theory of dark energy: A review

“…For example, it does not describe strong gravity nor higherdimensional regimes. The initial limitation of the EFT framework to include only DE/MG models based on a single scalar DoF was overcome recently by a proposal including additional vector and tensor fields [52]. We focus only on the original proposal encompassing DE/MG models with an extra scalar DoF in this review.…”

“…The panorama of theories that, despite the presence of higher derivatives in the equations of motions, avoid Ostrogradsky instabilities [47] has been exhausted by the Degenerate Higher Order Scalar-Tensor Theories (DHOST) [35,48,49,50]. In parallel, the original EFT formalism has been also extended to include those theories with second-order derivative equations of motion with a vector or tensor additional field [51,52], such as Generalised Proca [53], generalized Einstein-Aether [54] and massive bi-gravity [55]. Finally, while the EFT formalism was originally developed to describe general patterns of DE/MG models at linear cosmological scales, there has also been great progress in extending the framework to include non-linear perturbative effects [56,57,58,59,60,61].…”

Cosmological constraints on dark energy in light of gravitational wave bounds

“…In addition, note that the only dependence on c 2 s and D comes via the combination Dc 2 s , which (unlike the two terms separately) is independent of α K . So this is a direct manifestation of the well-understood fact that α K drops out in the QSA at leading order [18,35]. Both observables in (33) fundamentally constrain the (positive or vanishing) ratio of α 2 M and Dc 2 s .…”

“…3 below we show that P15 + LSS + GW and P15 + GW lead to near identical constraints. Dotted lines mark c i = 0 (the GR value), c B = 2 (a singular line physical models cannot cross in the α i = c i a parametrisation -see [34][35][36] for details) and c M = −c B (constraint derived from the GW prior). instability constraints introduces one additional class of interactions not constrained by current GW bounds [12].…”

“…The first three functions are as defined in [18,35] and we add β 4 here. With these definitions we can write the expression for the speed of sound c 2 s (12) in the following compact form…”