  Studying the effects of dark energy and modified gravity on cosmological
scales has led to a great number of physical models being developed. The
effective field theory (EFT) of cosmic acceleration allows an efficient
exploration of this large model space, usually carried out on a
phenomenological basis. However, constraints on such parametrized EFT
coefficients cannot be trivially connected to fundamental covariant theories.
In this paper we reconstruct the class of covariant Horndeski scalar-tensor
theories that reproduce the same background dynamics and linear perturbations
as a given EFT action. One can use this reconstruction to interpret constraints
on parametrized EFT coefficients in terms of viable covariant Horndeski
theories. We demonstrate this method with a number of well-known models and
discuss a range of future applications.
