In the last decades, a cosmological model that fits observations through a vast range of scales emerged. It goes under the name of $Lambda$CDM.
However, there are still challenging questions that remain unanswered by this model, such as what causes the observed accelerated expansion of the universe. Indeed, a cosmological constant is the simplest explanation, but its value is difficult to reconcile with our knowledge of quantum field theory. For this reason, many alternative models have been proposed, where the accelerated expansion is induced by a dynamical field or by a modification of general relativity. Independently on any theoretical prejudice, these models are testable and several missions have been planned for the next decade. These will highly improve the constraints on the deviations from the $Lambda$CDM model.
My thesis concerns an approach known as ``Effective Theory of Dark Energy''.
It is based on the idea that the large number of alternative models requires a simple, general and effective way to bridge theory and observations. It applies to all models where general relativity is modified by adding a single scalar degree of freedom.
There are various reasons why it is valuable. First, it is general enough, as in encompasses most of the existing models. Then, it parametrises directly the relevant degrees of freedom at the level of linear perturbations in cosmology, in a non-redundant way.
Finally, it is based on an action principle. Therefore, it allows a solid theoretical understanding of the viability of the theory.
The first part of the discussion will cover the more theoretical aspects. I will first review the most general class of scalar-tensor theories currently known. Then, I will introduce the effective description and show how it naturally encompass such theories. I will analyze the propagating degrees of freedom and address stability issues. Finally, I will show how to include a non-trivial coupling to matter in this framework.
The second part will be dedicated to describe some observable signatures of deviations from $Lambda$CDM. First, I will consider modifications of gravity combined to an interaction between dark matter and dark energy. I will provide an analytical understanding of the effects and analyze the constraining power that future experiments will have on the free parameters of the effective description.
Then, I will focus on theories where a kinetic mixing between matter and the scalar field is present. I will illustrate and quantify a peculiar feature they have, namely the weakening of gravity at scales relevant for redshift surveys.