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

Abstract

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.