Braneworld dynamics with the BraneCode

TL;DR

This paper presents a comprehensive numerical approach to 5D braneworld dynamics using the BraneCode, revealing phenomena like instability of static configurations, brane restructuring, and Kasner-like behavior during collisions.

Contribution

The paper introduces the BraneCode algorithm for solving nonlinear 5D braneworld equations and demonstrates its application to uncover novel dynamical phenomena.

Findings

Static warped geometries with de Sitter branes are often unstable.

Brane collisions lead to Kasner-like asymptotic geometries.

Re-structuring towards lower curvature configurations reduces the effective cosmological constant.

Abstract

We give a full nonlinear numerical treatment of time-dependent 5d braneworld geometry, which is determined self-consistently by potentials for the scalar field in the bulk and at two orbifold branes, supplemented by boundary conditions at the branes. We describe the BraneCode, an algorithm which we designed to solve the dynamical equations numerically. We applied the BraneCode to braneworld models and found several novel phenomena of the brane dynamics. Starting with static warped geometry with de Sitter branes, we found numerically that this configuration is often unstable due to a tachyonic mass of the radion during inflation. If the model admits other static configurations with lower values of de Sitter curvature, this effect causes a violent re-structuring towards them, flattening the branes, which appears as a lowering of the 4d effective cosmological constant. Braneworld dynamics can often lead to brane collisions. We found that in the presence of the bulk scalar field, the 5d geometry between colliding branes approaches a universal, homogeneous, anisotropic strong gravity Kasner-like asymptotic, irrespective of the bulk/brane potentials. The Kasner indices of the brane directions are equal to each other but different from that of the extra dimension.