Generating Scale-Invariant Perturbations from Rapidly-Evolving Equation of State

TL;DR

This paper explores a scalar field model that produces nearly scale-invariant perturbations, addressing non-gaussianity and quantum corrections, and proposes modifications to extend the observable scale range while maintaining consistency with observations.

Contribution

It demonstrates how to modify a scalar field potential to avoid perturbative breakdown and produce a broad, nearly scale-invariant, Gaussian perturbation spectrum compatible with observations.

Findings

Three-point function is scale dependent, causing perturbative issues on small scales.

Adjusting the potential suppresses small-scale power, avoiding perturbative breakdown.

The model can produce up to twelve e-folds of nearly scale-invariant, Gaussian modes.

Abstract

Recently, we introduced an ekpyrotic model based on a single, canonical scalar field that generates nearly scale invariant curvature fluctuations through a purely "adiabatic mechanism" in which the background evolution is a dynamical attractor. Despite the starkly different physical mechanism for generating fluctuations, the two-point function is identical to inflation. In this paper, we further explore this concept, focusing in particular on issues of non-gaussianity and quantum corrections. We find that the degeneracy with inflation is broken at three-point level: for the simplest case of an exponential potential, the three-point amplitude is strongly scale dependent, resulting in a breakdown of perturbation theory on small scales. However, we show that the perturbative breakdown can be circumvented -- and all issues raised in Linde et al. (arXiv:0912.0944) can be addressed -- by altering the potential such that power is suppressed on small scales. The resulting range of nearly scale invariant, gaussian modes can be as much as twelve e-folds, enough to span the scales probed by microwave background and large scale structure observations. On smaller scales, the spectrum is not scale invariant but is observationally acceptable.