Bouncing Negative-Tension Branes
Jean-Luc Lehners, Neil Turok
TL;DR
This work analyzes dynamical braneworlds with two domain walls of opposite tension, showing that a negative-tension brane can bounce before hitting a timelike naked singularity produced by a zero of the harmonic function. A key result is the necessary bounce condition $T^\mu_\mu + 3 \beta T_\phi > 0$, with a subdominant density-squared term, and the authors compare full 5D dynamics to a 4D moduli-space description across various brane-bound matter couplings. Scalar brane matter generally yields perfect agreement between 5D and 4D descriptions, while gauge fields and brane cosmological constants can expose limitations of the moduli-space approximation, particularly when the bulk geometry is kept unaltered. In heterotic M-theory, specific couplings (notably $C(\phi)=e^{\phi}$ for scalars and certain gauge-field couplings) enable robust bounces with minimal bulk modification, suggesting a stabilizing role for negative-tension branes in ekpyrotic/cyclic cosmologies and highlighting when a full 5D treatment is required.
Abstract
Braneworlds, understood here as double domain wall spacetimes, can be described in terms of a linear harmonic function, with kinks at the locations of the boundary branes. In a dynamical setting, there is therefore the risk that the boundary brane of negative tension, at whose location the value of the harmonic function is always lowest, can encounter a zero of this harmonic function, corresponding to the formation of a singularity. We show that for certain types of brane-bound matter this singularity can be avoided, and the negative-tension brane can shield the bulk spacetime from the singularity by bouncing back smoothly before reaching the singularity. In our analysis we compare the 5- and 4-dimensional descriptions of this phenomenon in order to determine the validity of the moduli space approximation.