Abstract
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 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.
Highlights
Modern theories suggest that the universe appears to have three spatial dimensions, there may be more
Regardless of the particular potential or exit method, the gist is that density perturbations in this approach set the bulk scale, and this scale will fall somewhere between the Planck scale and the electroweak scale depending on the details
From a physical point of view they are interesting because the large volume accounts for the weakness of four dimensional gravity, while the large mass gap makes the extra dimensions invisible in current experiments
Summary
Modern theories suggest that the universe appears to have three spatial dimensions, there may be more. Familiar intuition suggests that as the internal volume grows, it becomes energetically easier to excite modes in the extra directions–the mass gap to the Kaluza-Klein states decreases. This raises the question: why does the universe appear to be three dimensional? There is an extensive literature on the construction of hyperbolic surfaces of arbitrary genus that possess a large first eigenvalue: large in the sense that the lowest non-zero eigenvalue is bounded below by the curvature scale b−2, and is independent of the area even as the area goes to infinity for fixed b [11, 12, 13, 14, 15, 16]. The n-dimensional torus demonstrates the existence of a space that has the required large mass gap for both scalars and fermions
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