The consistency of codimension-2 braneworlds and their cosmology

TL;DR

This paper investigates the cosmology of codimension-2 braneworlds in 6D Lovelock gravity, focusing on matching conditions, energy exchange, and modified Friedmann equations, revealing self-acceleration and curvature effects.

Contribution

It clarifies the consistent matching conditions for codimension-2 branes and analyzes their cosmological implications, correcting previous assumptions in the literature.

Findings

Energy exchange between brane and bulk depends on regularisation.

Modified Friedmann equations include extrinsic curvature corrections.

Evidence of geometric self-acceleration and curvature effects.

Abstract

We study axially symmetric codimension-2 cosmology for a distributional braneworld fueled by a localised 4D perfect fluid, in a 6D Lovelock theory. We argue that only the matching conditions (dubbed topological) where the extrinsic curvature on the brane has no jump describe a pure codimension-2 brane. If there is discontinuity in the extrinsic curvature on the brane, this induces inevitably codimension-1 distributional terms. We study these topological matching conditions, together with constraints from the bulk equations evaluated at the brane position, for two cases of regularisation of the codimension-2 defect. First, for an arbitrary smooth regularisation of the defect and second for a ring regularisation which has a cusp in the angular part of the metric. For a cosmological ansatz, we see that in the first case the coupled system is not closed and requires input from the bulk equations away from the brane. The relevant bulk function, which is a time-dependent angular deficit, describes the energy exchange between the brane and the 6D bulk. On the other hand, for the ring regularisation case, the system is closed and there is no leakage of energy in the bulk. We demonstrate that the full set of matching conditions and field equations evaluated at the brane position are consistent, correcting some previous claim in the literature which used rather restrictive assumptions for the form of geometrical quantities close to the codimension-2 brane. We analyse the modified Friedmann equation and we see that there are certain corrections coming from the non-zero extrinsic curvature on the brane. We establish the presence of geometric self-acceleration and a possible curvature domination wedged in between the period of matter and self-acceleration eras as signatures of codimension-2 cosmology.