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.
Highlights
General Relativity (GR) [225, 226] is widely accepted as a fundamental theory to describe the geometric properties of spacetime
This burst of activities is strongly motivated by the observational discovery of dark energy
The idea is that the gravitational law may be modified on cosmological scales to give rise to the late-time acceleration, while Newton’s gravity needs to be recovered on solar-system scales
Summary
General Relativity (GR) [225, 226] is widely accepted as a fundamental theory to describe the geometric properties of spacetime. While scalar-field models of inflation and dark energy correspond to a modification of the energy-momentum tensor in Einstein equations, there is another approach to explain the acceleration of the universe This corresponds to the modified gravity in which the gravitational theory is modified compared to GR. For large coupling models with |Q| = O(1) it is possible to design scalar-field potentials such that the chameleon mechanism works to reduce the effective matter coupling, while at the same time the field is sufficiently light to be responsible for the late-time cosmic acceleration This generalized BD theory leaves a number of interesting observational and experimental signatures [596]. The Greek indices μ and ν run from 0 to 3, whereas the Latin indices i and j run from 1 to 3 (spatial components)
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