General brane cosmologies and their global spacetime structure
Peter Bowcock, Christos Charmousis, Ruth Gregory
TL;DR
This paper develops a fully general framework for brane cosmologies by treating the 4D Universe as a codimension-one wall of constant spatial curvature in a 5D spacetime. By solving the bulk Einstein equations in a static 5D background and applying Israel junction conditions, it identifies two bulk solution classes (class I and class II) and proves an equivalence between a fixed wall in a dynamic bulk and a moving wall in a static bulk, with the wall dynamics encoded in its trajectory and radion. The resulting generalized Friedmann-type equations and exact planar-wall solutions enable detailed analysis of cosmological trajectories for walls bordering Schwarzschild–AdS or vacuum spacetimes, including various criticality regimes and Z2-symmetric configurations, while highlighting radion effects and potential naked singularities in certain matchings. The framework provides a tractable, integrable approach to brane-world cosmology and perturbation theory, with implications for understanding radion dynamics and realistic brane scenarios such as GRS-like constructions.
Abstract
Starting from a completely general standpoint, we find the most general brane-Universe solutions for a three-brane in a five dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no assumptions other than the usual cosmological symmetries of the metric, we prove that the equations of motion form an integrable system, and find the exact solution. The cosmology is indeed a boundary of a (class II) Schwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the various cosmological trajectories focusing particularly on those bordering vacuum spacetimes. We find, not surprisingly, that not all cosmologies are compatible with an asymptotically flat spacetime branch. We comment on the role of the radion in this picture.