An effective description of dark energy: from theory to phenomenology
  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,
and many alternatives have been proposed. This thesis concerns an approach to
test such models known as "Effective Theory of Dark Energy" . It applies to all
models where general relativity is modified by adding a single scalar degree of
freedom, called "scalar-tensor theories". In Chapter 1 I summarise the most
general class of such theories currently known, called "Degenerate higher-Order
Scalar-Tensor" (DHOST) theories. In Chapter 2, I introduce the effective theory
of dark energy. The inclusion of a general coupling between matter and the
gravitational sector is the subject of Chapter 3. Chapter 4 analyses in details
the stability of different classes of theories. Notably, I show that the most
general class of theories free from instabilities reduces to the so-called
Horndeski and beyond-Horndeski theories, up to a non minimal coupling to
matter. Another goal of the thesis is to study the observable effects of
deviations from ${\Lambda}$CDM. In Chapter 5, I consider the possibility of an
interaction between dark matter and dark energy and I analyse the constraining
power of future surveys on the free parameters of the theory. Chapter 6 focuses
on the observational effects of theories where a kinetic mixing between matter
and the scalar field exists. This gives a peculiar and potentially observable
effect, namely the weakening of gravity at large scale structure scales.
