On the "Causality Argument" in Bouncing Cosmologies

TL;DR

It is shown that imposing causality is not sufficient to determine the spectrum of perturbations after a bounce provided it is known before, and consequences for string motivated scenarios are discussed.

Abstract

We exhibit a situation in which cosmological perturbations of astrophysical relevance propagating through a bounce are affected in a scale-dependent way. Involving only the evolution of a scalar field in a closed universe described by general relativity, the model is consistent with causality. Such a specific counter-example leads to the conclusion that imposing causality is not sufficient to determine the spectrum of perturbations after a bounce provided it is known before. We discuss consequences of this result for string motivated scenarios.

Figures (1)

• Figure 1: The effective potential $V_u(\eta)$ for the perturbation variable $u(\eta)$ as obtained by using the quartic expansion of the scale factor. The values $\eta_0=1.01$, $\delta=0$, and $\xi=-2/5$ have been used to derive this plot. The almost undistinguishable dot-dashed curve represents a rational approximation to this potential which is valid in the vicinity of the bounce and that is used in Ref. MP. Clearly, the potential is well-behaved at all relevant times, and so is the corresponding variable $u$.