Cosmology of codimension-two braneworlds

TL;DR

This work analyzes 6D codimension-two braneworld cosmologies with azimuthal symmetry, stabilized by bulk scalar fields or magnetic flux, containing at least one 3-brane. It classifies bulk solutions (Type 1–3) and derives brane jump conditions, showing that the 4D expansion rate can be unexpectedly independent of brane tension or depend nontraditionally on it. In warped AdS-soliton and unwarped football-shaped geometries, the authors compute how $\Lambda_4$ relates to brane tensions and stabilization parameters, revealing a nonstandard Friedmann relation and challenging the naive dimensional reduction picture. The analysis demonstrates a robust mechanism whereby the inner 2D geometry tunes away tension effects, while also outlining stability properties and the difficulties of achieving realistic cosmology within these models.

Abstract

We present a comprehensive study of the cosmological solutions of 6D braneworld models with azimuthal symmetry in the extra dimensions, moduli stabilization by flux or a bulk scalar field, and which contain at least one 3-brane that could be identified with our world. We emphasize an unusual property of these models: their expansion rate depends on the 3-brane tension either not at all, or in a nonstandard way, at odds with the naive expected dimensional reduction of these systems to 4D general relativity at low energies. Unlike other braneworld attempts to find a self-tuning solution to the cosmological constant problem, the apparent failure of decoupling in these models is not associated with the presence of unstabilized moduli; rather it is due to automatic cancellation of the brane tension by the curvature induced by the brane. This provides some corroboration for the hope that these models provide a distinctive step toward understanding the smallness of the observed cosmological constant. However, we point out some challenges for obtaining realistic cosmology within this framework.