Petrov A. Introduction to Modified Gravity

Springer, 2020. — 77 p. — (Springer Briefs in Physics). — 10.1007/978-3-031-46634-2This review presents itself as a collection of the lecture notes on modified gravity
based on lectures given at UFPB (Joao Pessoa, Brazil), CBPF (Rio de Janeiro, Brazil), UFC (Fortaleza, Brazil), and Universidad del Bio-Bio (Concepcion, Chile). General relativity (GR) is clearly one of the most successful physical theories. Being formulated as a natural development of the special relativity, it has made a number of fundamental physical predictions which have been confirmed experimentally with a very high degree of precision. Among these predictions, the special role is played by expansion of the Universe and precession of Mercure perihelion, which have been proved many years ago, while other important claims of GR such as gravitational waves and black holes, have been confirmed through direct observations only recently. By its concept, the general relativity is an essentially geometric theory. Its key
idea consists in the fact that the gravitational field manifests itself through modifications of the space-time geometryEinstein Gravity and the Need for Its Modification
Modifications of the Pure Gravitational Sector
Scalar-Tensor Gravities
Vector-Tensor Gravities and Problem of Lorentz Symmetry Breaking in Gravity
Horava–Lifshitz Gravity
Nonlocal Gravity
Summary