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 apply the BRANECODE to braneworld models and find several novel phenomena of the brane dynamics. Starting with static warped geometry with de Sitter branes, we find 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 restructuring 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 find 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 or brane potentials. The Kasner indices of the brane directions are equal to each other but different from that of the extra dimension.
Johannes, Martin; Felder, Gary; Frolov, Andrei V.; Peloso, Marco; and Kofman, Lev, "Braneworld dynamics with the BRANECODE" (2004). Physics: Faculty Publications, Smith College, Northampton, MA.