Sourced fluctuations in generic slow contraction

TL;DR

This paper explores the conditions for super horizon freeze-out in slow contracting universes, focusing on sourced perturbations, and finds that typical fast-roll models predict a tensor-to-scalar ratio incompatible with observations, requiring alternative sources or deviations.

Contribution

It establishes generic conditions for super horizon freeze-out in slow contraction and analyzes the limitations of fast-roll sourced bounce models in matching observational data.

Findings

Fast-roll models predict r ≈ 1/9, inconsistent with current constraints.

A viable red scalar spectrum can be achieved with specific scalar-gauge couplings.

Small modifications in fast-roll do not reduce r below 0.06 for more than an e-fold.

Abstract

We introduce a set of generic conditions for the slow contracting Universe and for a narrowed-down category of models called fast-roll models. We present general conditions for super horizon freeze-out of scalar and tensor perturbations and show that any fast-roll model satisfies them, as in the case of inflation. We are interested in the "Sourced Bounce" scenario, where perturbations are sourced by a $U(1)$ gauge field coupled to a bouncer scalar field. The requirement of a slightly red tilted scalar spectrum greatly restricts the allowed couplings between the scalar and the gauge field. We show that a viable slightly red scalar spectrum is achievable. However, within the fast-roll approximation, the tensor-to-scalar ratio is in general $r\simeq 1/9$, inconsistent with current observations. We demonstrate the general result with an explicit example we dub "Intermediate contraction". We prove that small modifications in fast-roll that do not alter the Green's functions do not result in $r<0.06$ consistent with the data for more than an e-fold. Hence, a successful "Sourced Bounce" requires a different source or a significant deviation from fast-roll.