Non-linear vector perturbations in a contracting universe

TL;DR

This paper investigates second order vector perturbations in contracting universe models, showing they are generated by scalar mode couplings and could be significantly different from inflationary predictions, potentially distinguishing these scenarios.

Contribution

It provides explicit expressions for second order vector perturbations in contracting universes and compares their magnitudes with inflationary cases, highlighting possible observational differences.

Findings

Vector perturbations are generated by scalar mode couplings in contracting models.

The magnitude of these perturbations can be large and grow with collapse duration.

Differences depend on collapse details and how the hot big bang is recovered.

Abstract

A number of scalar field models proposed as alternatives to the standard inflationary scenario involve contracting phases which precede the universe's present phase of expansion. An important question concerning such models is whether there are effects which could potentially distinguish them from purely expanding cosmologies. Vector perturbations have recently been considered in this context. At first order such perturbations are not supported by a scalar field. In this paper, therefore, we consider second order vector perturbations. We show that such perturbations are generated by first order scalar mode-mode couplings, and give an explicit expression for them. We compare the magnitude of vector perturbations produced in collapsing models with the corresponding amplitudes produced during inflation, using a number of suitable power-law solutions to model the inflationary and collapsing scenarios. We conclude that the ratios of the magnitudes of these perturbations depend on the details of the collapsing scenario as well as on how the hot big bang is recovered, but for certain cases could be large, growing with the duration of the collapse.