Generating Ekpyrotic Curvature Perturbations Before the Big Bang

TL;DR

The paper demonstrates that a contracting pre-big-bang phase can produce a nearly scale-invariant curvature perturbation spectrum entirely within 4d effective field theory by generating entropy perturbations in a multi-field ekpyrotic background and converting them to curvature perturbations near a crunch. Gravity adds a small blue correction to the entropy tilt, while the non-gravitational (scale-invariant) part tends to be red, yielding an overall tilt $n_s$ typically in the range $0.97$ to $1.02$ for simple models. The conversion mechanism—via a bounce off a boundary in moduli space—transfers the entropy spectrum to curvature perturbations with an amplitude compatible with observations (requiring a GUT-scale energy scale near the minimum of the potential) and predicts a distinctive tilt signature that can help distinguish this scenario from inflation. The approach generalizes beyond specific higher-dimensional realizations, offering a robust, testable alternative for the origin of cosmic structure in pre-big-bang cosmologies.

Abstract

We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, that can be entirely described using 4d effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyrotic models in which the big bang is modelled as a brane collision, as well as other types of cosmological models with a pre-big bang phase. We show that the correct perturbation amplitude can be obtained and that the scalar spectral tilt n tends to range from slightly blue to red, with 0.97 < n < 1.02 for the simplest models, a range compatible with current observations but shifted by a few per cent towards the blue compared to the prediction of the simplest, large-field inflationary models.