This unique thesis covers all aspects of
theories of gravity beyond Einstein's General Relativity, from setting up the
equations that describe the evolution of perturbations, to determining the
best-fitting parameters using constraints like the microwave background
radiation, and ultimately to the later stages of structure formation using
state-of-the-art N-body simulations and comparing them to observations of
galaxies, clusters and other large-scale structures. This truly ground-breaking
work puts the study of modified gravity models on the same footing as the
standard model of cosmology. Since the discovery of the accelerating expansion
of the Universe, marked by the awarding of the 2011 Nobel Prize in Physics,
there has been a growing interest in understanding what drives that
acceleration. One possible explanation lies in theories of gravity beyond
Einstein's General Relativity. This thesis addresses all aspects of the problem,
an approach that is crucial to avoiding potentially catastrophic biases in the
interpretation of upcoming observational missions.