  We present the extension of the effective field theory framework to the
mildly non-linear scales. The effective field theory approach has been
successfully applied to the late time cosmic acceleration phenomenon and it has
been shown to be a powerful method to obtain predictions about cosmological
observables on linear scales. However, mildly non-linear scales need to be
consistently considered when testing gravity theories because a large part of
the data comes from those scales. Thus, non-linear corrections to predictions
on observables coming from the linear analysis can help in discriminating among
different gravity theories. We proceed firstly by identifying the necessary
operators which need to be included in the effective field theory Lagrangian in
order to go beyond the linear order in perturbations and then we construct the
corresponding non-linear action. Moreover, we present the complete recipe to
map any single field dark energy and modified gravity models into the
non-linear effective field theory framework by considering a general action in
the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we
proceed to map the beyond-Horndeski theory and low-energy Horava gravity into
the effective field theory formalism. As a final step we derived the 4th order
action in term of the curvature perturbation. This allowed us to identify the
non-linear contributions coming from the linear order perturbations which at
the next order act like source terms. Moreover, we confirm that the stability
requirements, ensuring the positivity of the kinetic term and the speed of
propagation for scalar mode, are automatically satisfied once the viability of
the theory is demanded at linear level. The approach we present here will allow
to construct, in a model independent way, all the relevant predictions on
observables at mildly non-linear scales.
