Introduction

The topics that have been discussed in this volume are generally very difficult ones. They involve some of the big questions that philosophers have pondered for centuries. The wonderful thing about physics is that sometimes, by pondering “little” tractable problems, you uncover deep truths. Little inconsistencies or new results from old theories can lead to wisdom. These advances are not anticipated but by having the big questions in mind, one recognizes them when they appear.

In trying to understand deeper truths about cosmology, extra dimensions are a good place to begin. The equations are well grounded in general relativity at scales where quantum gravitational effects should be under control. Nevertheless, by not exclusively focusing on four–dimensional cosmological solutions, one can discover new phenomena. These might even lead to fundamental truths that can impinge on the four-dimensional appearing universe that we observe.

The plan of this chapter is to first go over some of the major questions in cosmology. I will then discuss some new gravitational solutions in more than four dimensions, and what new aspects of gravity they reveal. The other nice thing about these solutions is that they can be used as a testing ground for ideas about gravity that have been developed based on four-dimensional intuition. I will then sketch some of the newer developments in extra dimensions, and how new geometries continue to reveal unanticipated features.