# Curvature perturbations from ekpyrotic collapse with multiple fields

## TL;DR

This paper demonstrates how multiple-field ekpyrotic models generate scale-invariant isocurvature perturbations during collapse, which are converted into curvature perturbations at the transition to single-field dominance, with amplitude set by the Hubble scale.

## Contribution

It shows that the transition from multi-field to single-field ekpyrotic collapse naturally converts isocurvature to curvature perturbations, providing a mechanism for primordial perturbation generation.

## Key findings

- Scale-invariant isocurvature spectrum generated during collapse
- Conversion of isocurvature to curvature perturbations at transition
- Final perturbation amplitude linked to Hubble scale

## Abstract

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in the ekpyrotic scaling solution in models where multiple fields have steep negative exponential potentials. The scale invariance of the spectrum is realized by a tachyonic instability in the isocurvature field. This instability drives the scaling solution to the late time attractor that is the old ekpyrotic collapse dominated by a single field. We show that the transition from the scaling solution to the single field dominated ekpyrotic collapse automatically converts the initial isocurvature perturbations about the scaling solution to comoving curvature perturbations about the late-time attractor. The final amplitude of the comoving curvature perturbation is determined by the Hubble scale at the transition.