Semi-dynamical perturbations of unified dark energy

TL;DR

This paper introduces a semi-dynamical approach to analyze linear cosmological perturbations in unified dark energy and modified gravity models, improving beyond quasistatic approximations especially near the Hubble scale.

Contribution

It presents a semi-dynamical method for studying perturbations that extends the quasistatic approximation to include near-Hubble scale effects in a broad class of models.

Findings

Good agreement with full perturbation calculations

Effective for Horndeski and beyond-Horndeski theories

Accounts for corrections near the Hubble scale

Abstract

Linear cosmological perturbations of a large class of modified gravity and dark energy models can be unified in the effective field theory of cosmic acceleration, encompassing Horndeski scalar-tensor theories and beyond. The fully available model space inherent to this formalism cannot be constrained by measurements in the quasistatic small-scale regime alone. To facilitate the analysis of modifications from the concordance model beyond this limit, we introduce a semi-dynamical treatment extrapolated from the evolution of perturbations at a pivot scale of choice. At small scales, and for Horndeski theories, the resulting modifications recover a quasistatic approximation but account for corrections to it near the Hubble scale. For models beyond Horndeski gravity, we find that the velocity field and time derivative of the spatial metric potential can generally not be neglected, even in the small-scale limit. We test the semi-dynamical approximation against the linear perturbations of a range of dark energy and modified gravity models, finding good agreement between the two.