Screening and degenerate kinetic self-acceleration from the nonlinear freedom of reconstructed Horndeski theories

Abstract

We have previously presented a reconstruction of Horndeski scalar-tensor theories from linear cosmological observables. It includes free nonlinear terms which can be added onto the reconstructed covariant theory without affecting the background and linear dynamics. After discussing the uniqueness of these correction terms, we apply this nonlinear freedom to a range of different applications. First we demonstrate how the correction terms can be configured to endow the reconstructed models with screening mechanisms such as the chameleon, k-mouflage and Vainshtein effects. A further implication is the existence of classes of Horndeski models that are degenerate with standard cosmology to an arbitrary level in the cosmological perturbations. Particularly interesting examples are kinetically self-accelerating models that mimic the dynamics of the cosmological constant to an arbitrary degree in perturbations. Finally, we develop the reconstruction method further to the level of higher-order effective field theory, which under the restriction to a luminal propagation speed of gravitational waves introduces two new free functions per order. These functions determine the corresponding correction terms in the linearly reconstructed action at the same order. Our results enable the connection of linear cosmological constraints on generalised modifications of gravity and dark energy with the nonlinear regime and astrophysical probes for a more global interpretation of the wealth of forthcoming cosmological survey data.

Effective field theory of dark energy: A review

“…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].…”

Tailoring cosmologies in cubic shift-symmetric Horndeski gravity

“…The existence of Vainshtein screening in galileon gravity is well-known and the question of its applicability and other screening mechanisms to cubic Horndeki with vanishing scalar current is something that we intend to address in a future paper. One potentially useful framework for testing Horndeski theories against cosmological observables has been laid down as the effective field theory of dark energy [80][81][82][83][84][85][86][87]. In this approach, the background dynamics is reduced to a set of constant coefficients in front of the perturbations and the analysis is carried out agnostic of the background, i.e.…”

Positivity bounds on reconstructed Horndeski models

“…where the set of functions {ξ (2,3) n (φ)} are completely free in the absence of nonlinear information. They can be used to, for example, implement screening mechanisms in the reconstructed theory [42]. The key property they possess in the context of this paper is that they vanish on the background solution for the scalar field φ = tM 2 * as here X = X 0 = −M 4 * .…”

“…For example, using this approach Ref. [42] demonstrated how to implement screening mechanisms in theories that are only constrained at the level of the linear perturbations.…”