Semi-dynamical perturbations of unified dark energy
  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.
