Nonlinear aspects of the effective theory of dark energy

The goal of this project is to study the effects predicted by scalar-tensor theories of dark energy on small scales. Scalar-tensor theories has been introduced to modify gravity in the infrared. However, large scale modifications of gravity are necessarily associated to short-scale ones. In order to be in accordance with current observational tests on small scales, one can introduce a screening mechanism that is effective in environments where nonlinearities of the scalar field become important, suppressing the extra degrees of freedom. The Vainshtein screening has been already proven to work in many scalar-tensor theories, in particular in the most general second-order covariant theory for gravity coupled to a scalar degree of freedom, the so-called Horndeski theory. The focus of this thesis is on the breaking of this mechanism in the extensions of Horndeski: we retrieve the failure of the screening for beyond Horndeski theories, starting from more general premises. Finally, we tackle the challenge of generalizing this result further to DHOST theories.