A Critical Cosmological Constant from Millimeter Extra Dimensions

TL;DR

This paper proposes a mechanism in a six-dimensional brane-world with two large extra dimensions in which the bulk geometry makes the effective four-dimensional cosmological constant insensitive to standard-model brane tensions. The approach relies on a conical deficit in the transverse space and a warp factor, but a range of non-singular compactification schemes fail to preserve this decoupling, often culminating in naked singularities that hint at necessary Planck-scale physics. An effective-field-theory analysis shows Standard Model loop contributions to the 4D cosmological constant can be cut off at the millimeter scale, yielding $\Lambda_{4,\mathrm{eff}} \sim \ell^{-4}/(16\pi^2)$ and potentially placing it in the cosmologically favored range for $\ell \sim 10^{-2}$ mm. Although not a complete solution to the cosmological constant problem, the framework offers a testable link between millimeter-scale extra dimensions, gravity at short distances, and high-energy experiments, and it motivates further exploration of bulk symmetries and the role of Planck-scale physics near singularities.

Abstract

We consider `brane universe' scenarios with standard-model fields localized on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is rotationally symmetric about the brane, local quantities in the bulk are insensitive to the couplings on the brane. This potentially allows compactifications where the effective 4-dimensional cosmological constant is independent of the couplings on the 3-brane. We consider several possible singularity-free compactification mechanisms, and find that they do not maintain this property. We also find solutions with naked spacetime singularities, and we speculate that new short-distance physics can become important near the singularities and allow a compactification with the desired properties. The picture that emerges is that standard-model loop contributions to the effective 4-dimensional cosmological constant can be cut off at distances shorter than the compactification scale. At shorter distance scales, renormalization effects due to standard-model fields renormalize the 3-brane tension, which changes a deficit angle in the transverse space without affecting local quantities in the bulk. For a compactification scale of order 10^{-2} mm, this gives a standard-model contribution to the cosmological constant in the range favored by cosmology.