Perturbations in bouncing cosmologies: dynamical attractor vs scale invariance

TL;DR

The paper investigates whether density perturbations in ekpyrotic/cyclic bouncing cosmologies can be predicted robustly, independent of the unknown bounce physics. By comparing gauges and highlighting a dynamical attractor in the contracting phase, it argues that local observables follow the unperturbed solution up to exponentially small corrections, enabling (in principle) non-linear evolution through the bounce. However, under the key assumption that bounce physics is not overly sensitive to these tiny corrections, the resulting spectrum is not scale invariant and thus incompatible with observations. The non-linear analysis in synchronous gauge reinforces that, with the attractor, predictions are determined by the pre-bounce evolution and remain not scale invariant, placing strong constraints on such bouncing scenarios unless new high-energy physics alters the bounce behavior. Overall, the work clarifies gauge-dependent issues in perturbation theory through a bounce and shows that scale-invariant predictions are not generic in these models unless the UV bounce physics is finely tuned or fundamentally different from the scenario analyzed.

Abstract

For bouncing cosmologies such as the ekpyrotic/cyclic scenarios we show that it is possible to make predictions for density perturbations which are independent of the details of the bouncing phase. This can be achieved, as in inflationary cosmology, thanks to the existence of a dynamical attractor, which makes local observables equal to the unperturbed solution up to exponentially small terms. Assuming that the physics of the bounce is not extremely sensitive to these corrections, perturbations can be evolved even at non-linear level. The resulting spectrum is not scale invariant and thus incompatible with experimental data. This can be explicitly shown in synchronous gauge where, contrary to what happens in the commonly used Newtonian gauge, all perturbations remain small going towards the bounce and the existence of the attractor is manifest.