Effective description of higher-order scalar-tensor theories

Abstract

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called "beyond Horndeski" theories. We also discuss Lorentz-breaking models inspired by Horava gravity.

A covariant Lagrangian for stable nonsingular bounce

“…(A.6) by using formulae given in eqs. (2.14) of [24]. According to the above results, our model (3.1) belongs to a subclass of the DHOST theory with α L = 0 and α T = 0.…”

“…(A.5) extra conditions on the functions a A and b A need to be satisfied so that there is no extra propagating degree of freedom, see [24] and references therein for further discussions.…”

“…In the EFT formalism, the quadratic action for DHOST theory can be written as where δN = δg 00 /2, δ 2 R (3) stands for the second order term in the perturbative expansion of R (3) , the dimensionless time-dependent functions α L , α T , α K , α B , α H , β 1 , β 2 and β 3 satisfy certain conditions so that there is no extra propagating degree of freedom, see [24] for details.…”

“…Moreover, the developments of scalar-tensor theory (the GLPV [21] and DHOST theory [22][23][24], the mimetic gravity [25,26]) might also be able to provide us with some chances to implement stable nonsingular cosmologies. However, due to the complexity of relevant theories, which component is required for a stable bounce is not clear.…”

Reining in Alternative Gravity

“…DHOST theories are constructed to be a further generalization of Horndeski, but have to include new constraints to avoid Ostrogradsky instabilities. The result is a long list of classes of theories (≃30) having disjoint parameter spaces, but which on a cosmological background reduce to just two types [43]. One is unstable and thus irrelevant here.…”