This thesis presents significant new results on the problem of understanding the origin of dark energy in cosmology. The work develops an original approach based on modifications of General Relativity at cosmological scales, introducing non -local effective terms that can in principle emerge from fundamental local theories. Both the phenomenological consequences and theoretical aspects of the proposal are developed in depth. The thesis also contains significant new material compared to that published by the author in scientific journals.

This thesis presents significant new results on the problem of understanding the origin of dark energy in cosmology. The work develops an original approach based on modifications of General Relativity at cosmological scales, introducing non -local effective terms that can in principle emerge from fundamental local theories. Both the phenomenological consequences and theoretical aspects of the proposal are developed in depth. The thesis also contains significant new material compared to that published by the author in scientific journals.

This book presents a novel mathematical formalism, based on the tetrad formulation of differential geometry, for describing cosmological observables exactly and conveniently. It covers all the standard observables, i.e. distances, weak lensing, number counts and cosmic microwave background, and also includes a detailed derivation of general-relativistic matrix kinetic theory. All the fully nonlinear equations are derived in detail and the mathematical content is self-contained, so that readers require only a basic knowledge of general relativity. Moreover, the authors discuss several subtle issues that are usually overlooked in the literature and, in particular, issues that distinguish this formalism from the more approximative standard practice.