Modified Theories of Gravity and Cosmological Applications

General relativity is a theory of gravity that describes with high accuracy some of the effects of gravity, such as solar system tests, gravitational lensing, gravitational waves, black holes, etc., in a definite framework of homogeneous and isotropic space-time.However, considering the abundance and nature of dark energy and dark matter, the nature of inflation, cosmological tensions such as the H0 and S8, the possible values of local anisotropy in the evolution of the Universe, as well as the theoretical problems of the cosmological constant and of non-renormalizability, the validity range of general relativity might be restricted. Modified theories of gravity extend the form of general relativity through various methods, leading to different field equations and thus to different cosmological implications. They play an essential role in and contribute to modern cosmology, providing a foundation for the current understanding of physical phenomena of the Universe.