Modifying gravity: Cosmic acceleration and the large scale structure of the universe

The late time acceleration of the universe poses a puzzle for modern cosmology. There exist several independent pieces of evidence pointing at cosmic acceleration, but we do not have yet a compelling theoretical explanation for it. General relativity applied to a universe that is homogeneous and isotropic on large scales and which contains only radiation and matter does not fit the observations. Assuming homogeneity and isotropy describes correctly the universe on large scales (as many observations indicate), the solution to this puzzle requires postulating either a new energy component, dark energy (be it the cosmological constant or a smoothly distributed dynamical field), or new gravitational dynamics on large scales - modified gravity . In this thesis we focus on the latter approach and investigate models of modified gravity in the context of cosmic acceleration. In particular, we consider f ( R ) theories, in which the action for gravity is a general function of the Ricci scalar R , as well as constructing and studying a model inspired by these theories, which we dubbed Modified-Source Gravity. For both theories we study in detail the cosmology of the homogeneous and isotropic background, to determine whether and under which conditions the models display a viable expansion history and satisfy the constraints imposed by local tests of gravity. We then proceed to study the evolution of the inhomogeneities around the background, which ultimately form large scale structure via gravitational instability. We apply the theory of cosmological perturbation to linear order in the fluctuations and derive predictions for the growth of structure. We find that, in these theories of modified gravity, at the background level, there is sufficient freedom to reproduce the desired expansion history, and that this leads to a degeneracy between modified gravity and dark energy models. Nevertheless, at the level of large scale structure the modifications induce a peculiar scale dependent pattern of growth and the degeneracy may be broken. We find indeed that the Newton constant describing the clustering of dark matter is rescaled in a time- and scale-dependent way and can depart significantly from its general relativity value at late times on sufficiently small scales. Another peculiar feature common to the models we study is the introduction of a slip between the Newtonian potentials as well as a modification of their time dependence on small scales. After identifying the signatures of the modifications at the level of large scale structure, we briefly give an overview of current and future surveys that could offer important tests of gravity