Reconstructing Horndeski theories from phenomenological modified gravity
  and dark energy models on cosmological scales
  Recently we have derived a set of mapping relations that enables the
reconstruction of the family of Horndeski scalar-tensor theories which
reproduce the background dynamics and linear perturbations of a given set of
effective field theory of dark energy coefficients. In this paper we present a
number of applications of this reconstruction. We examine the form of the
underlying theories behind different phenomenological parameterizations of
modified gravity and dark energy used in the literature, as well as examine
theories that exhibit weak gravity, linear shielding, and minimal
self-acceleration. Finally, we propose a new inherently stable parametrization
basis for modified gravity and dark energy models.
