Modified Gravity in Higher Dimensions, Flux Compactification, and Cosmological Inflation

We review a possible origin of cosmological inflation from higher ( D ) spacetime dimensions in the context of modified gravity theory. It is demonstrated that it requires a spontaneous warped compactification of higher ( D ) spacetime dimensions together with the stabilization of extra ( D − 4 ) dimensions by Freund–Rubin mechanism. The relevant tools include an extra gauge ( D / 2 − 1 ) -form field with a non-vanishing flux in compact dimensions and a positive cosmological constant in D dimensions. Those features are illustrated on the specific example in eight spacetime dimensions compactified on a four-sphere with a warped factor and a flux, which leads to a viable Starobinsky-like inflationary model in four (non-compact) spacetime dimensions.

f(R) Theories

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.