Theoretical cosmology is a vastly developing science, bringing a fundamental link between particle physics, theoretical physics and astrophysics. Its recent success and huge increase of publications are related to the fact that we are living in the era of the so-called precision cosmology. Hence, more and more accurate bounds are obtained on the cosmological parameters through the whole cosmic history, starting from the Big Bang up to the currently observed Universe. Observational confirmations for the early and late accelerations come from data related to the cosmic microwave background, the large scale structure, the baryonic acoustic oscillations, the supernovae, the Hubble flow, the gravitational lensing, among others. The overall picture of the Universe is that of an accelerating dynamical system dominated by some cosmic fluids giving rise to the current ‘speed up’ (dark energy or cosmological constant), a dark matter component accounting for the clustering and the stability of structures, and some percentage of luminous matter, radiation and neutrinos.

Several questions arise about the basic gravitational theory which governs the cosmic evolution. The above observations point out that either most of the Universe content is unknown (and then the problem of dark energy and dark matter should be solved from the particle physics side) or General Relativity should be reviewed in view of some extension, retaining the good results at local scales and addressing the ultraviolet and infrared problems at cosmic scales. At best, General Relativity is a reasonable approximation for the description of the Universe evolution at local scales. However, it should be qualitatively modified, especially at the very early (ultraviolet) scales and, eventually, at the current and even at the future epochs (infrared scales). This revision can be related to the three not yet understood components of the universe, specifically inflation, dark matter and dark energy.

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The volume can represent a useful overview on the current status of General Relativity and the fundamental questions which are still open in theoretical cosmology and in the foundations of gravitational physics. It aims to be an overall and self-contained work that, without any claim of completeness, could be a useful research instrument.