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f(R) theories

TLDR
Various applications of f(R) theories to cosmology and gravity — such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds are reviewed.
Abstract
Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

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Modified Gravity and Cosmology

TL;DR: A comprehensive survey of recent work on modified theories of gravity and their cosmological consequences can be found in this article, where the authors provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a selfcontained, comprehensive and up-to-date introduction to the subject as a whole.
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Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

TL;DR: In this article, the structure and cosmological properties of a number of modified theories, including traditional F (R ) and Hořava-Lifshitz F ( R ) gravity, scalar-tensor theory, string-inspired and Gauss-Bonnet theory, non-local gravity, nonminimally coupled models, and power-counting renormalizable covariant gravity are discussed.
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The Confrontation Between General Relativity and Experiment

TL;DR: Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging.
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Extended Theories of Gravity

TL;DR: Extended Theories of Gravity as discussed by the authors can be considered as a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales, which is an approach that, by preserving the undoubtedly positive results of Einstein's theory, is aimed to address conceptual and experimental problems recently emerged in astrophysics, cosmology and High Energy Physics.
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$f(R,T)$ gravity

TL;DR: In this article, the authors considered a modified theory of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and of the trace of the stress-energy tensor.
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