Clarifying perturbations in the ekpyrotic universe

TL;DR

This note tackles the problem of perturbation transfer across the ekpyrotic contracting-to-expanding transition. It develops a general four-dimensional matching framework based on Israel junction conditions and analyzes how the choice of matching surface affects which perturbation modes survive into the expansion. The key result is that different prescriptions—matching on constant energy density in longitudinal gauge versus continuity of comoving energy perturbations—lead to different inheritance of the contracting growing mode, clarifying the source of the competing claims in the literature. The analysis emphasizes that a full resolution requires a five-dimensional treatment to determine the surface stress density and its fluctuations, with the implication that the scale-invariant mode may persist as a homogeneous contribution, though its dominance remains uncertain. The work sharpens the theoretical understanding of perturbations in brane-collision cosmologies and guides future multidimensional analyses.

Abstract

In this note I try to clarify the problem of perturbations in the ekpyrotic universe. I write down the most general matching conditions and specify the choices taken by the two debating sides. I also bring up the problem of surface stresses which always have to be present when a transition from a collapsing to an expanding phase is made.