Cosmological matching conditions

TL;DR

This paper studies how scalar metric perturbations evolve during sudden cosmological transitions, especially considering inhomogeneous surface stresses and their effects on perturbation continuity.

Contribution

It derives matching conditions for scalar perturbations across sudden transitions with inhomogeneous stresses, highlighting the role of entropy perturbations.

Findings

Comoving curvature perturbation remains continuous for adiabatic perturbations.

Newtonian potential can be discontinuous if background expansion rate jumps.

Surface stress perturbations depend on intrinsic entropy perturbations of scalar fields.

Abstract

We investigate the evolution of scalar metric perturbations across a sudden cosmological transition, allowing for an inhomogeneous surface stress at the transition leading to a discontinuity in the local expansion rate, such as might be expected in a big crunch/big bang event. We assume that the transition occurs when some function of local matter variables reaches a critical value, and that the surface stress is also a function of local matter variables. In particular we consider the case of a single scalar field and show that a necessary condition for the surface stress tensor to be perturbed at the transition is the presence of a non-zero intrinsic entropy perturbation of the scalar field. We present the matching conditions in terms of gauge-invariant variables assuming a sudden transition to a fluid-dominated universe with barotropic equation of state. For adiabatic perturbations the comoving curvature perturbation is continuous at the transition, while the Newtonian potential may be discontinuous if there is a discontinuity in the background Hubble expansion.