Self-gravitating branes again

TL;DR

This paper questions the standard Israel matching conditions for branes, proposes alternative conditions that include back-reaction effects, and demonstrates their consistency and cosmological implications in higher-dimensional gravity models.

Contribution

It introduces new matching conditions for branes that incorporate back-reaction by varying the embedding fields, addressing limitations of traditional conditions in higher codimensions.

Findings

Alternative matching conditions are consistent for codimension-2 branes in 6D EGB gravity.

Cosmological solutions exhibit LFRW behavior with corrections, avoiding singularities.

Effective cosmological constant naturally emerges from the model parameters.

Abstract

We raise on theoretical grounds the question of the physical relevance of Israel matching conditions and their generalizations to higher codimensions, the standard cornerstone of the braneworld and other membrane scenarios. Our reasoning is twofold: First, the incapability of the conventional matching conditions to accept the Nambu-Goto probe limit (even the geodesic limit of the Israel matching conditions is not acceptable since being the geodesic equation a kinematical fact it should be preserved for all gravitational theories or defects, which is not the case for these conditions). Second, in our D-dimensional spacetime (maybe D=4), classical defects of any possible codimension should be compatible. These matching conditions fail to accept codimension-2 and 3 defects for D=4 (which represents effectively the spacetime at certain length and energy scales) and most probably fail to accept high enough codimensional defects for any D since there is no high enough Lovelock density to support them. Here, we propose alternative matching conditions which seem to satisfy the previous criteria. Instead of varying the brane-bulk action with respect to the bulk metric at the brane position, we vary with respect to the brane embedding fields so that the gravitational back-reaction is included. For a codimension-2 brane in 6-dim EGB gravity we prove its consistency for an axially symmetric cosmological configuration. The cosmologies found have the LFRW behaviour and extra correction terms. For a radiation brane one solution avoids a cosmological singularity and undergoes accelerated expansion near the minimum scale factor. In the presence of an induced gravity term, there naturally appears in the theory the effective cosmological constant scale lambda/(M_6^4 r_c^2), which for a brane tension lambda\sim M_6^4 (e.g. TeV^4) and r_c \sim H_0^{-1} gives the observed value of the cosmological constant.