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

Sergei V Ketov

doi:10.3390/sym11121528

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.

Highlights

Einstein’s theory of general relativity is the best example of power of the general covariance
It was the important extension of the old Kaluza–Klein (KK) idea motivated by the unification of fundamental forces because extra dimensions appear in field theory and gravity, supersymmetry and supergravity, as well as string theory and braneworld
In this paper we review the inflationary models based on modified gravity in various dimensions, and emphasize the role of warped metric and flux compactification for theoretical consistency and phenomenological applications

Summary

Introduction

Einstein’s theory of general relativity is the best example of power of the general covariance. Amongst the natural constraints to be imposed are (i) spontaneous compactification, i.e., the requirement of a compactified theory to obey the equations of motion of the higher-dimensional theory, (ii) stabilization of extra dimensions, in order to ensure the visible four-dimensional universe with a long lifetime, (iii) a viable hierarchy of fundamental scales, and (iv) consistency with observations. This list can be extended by demanding a realization of viable inflation in the early universe from higher dimensions.

Starobinsky Model of Inflation

Modified Gravity and Inflaton Scalar Potential in D Dimensions

B A f BB f d

Freund–Rubin Compactification

Study of the Scalar Potential

The Inflationary Observables

Conclusions