  The universe may have extra spatial dimensions with large volume that we
cannot perceive because the energy required to excite modes in the extra
directions is too high. Many examples are known of such manifolds with a large
volume and a large mass gap. These compactifications can help explain the
weakness of four-dimensional gravity and, as we show here, they also have the
capacity to produce reasonable potentials for an inflaton field. Modeling the
inflaton as a bulk scalar field, it becomes very weakly coupled in four
dimensions, and this enables us to build phenomenologically acceptable
inflationary models with tunings at the few per mil level. We speculate on dark
matter candidates and the possibility of braneless models in this setting.
