Generating Scale-Invariant Perturbations from Rapidly-Evolving Equation of State
Justin Khoury, Paul J. Steinhardt
TL;DR
<3-5 sentence high-level summary> The paper investigates a single-field adiabatic ekpyrotic mechanism that generates a scale-invariant curvature perturbation spectrum through a dynamical attractor during a rapid ε-transition on a nearly static background, highlighting its inflationary degeneracy at the two-point level. It then shows that the degeneracy is broken at the three-point level by a strongly scale-dependent non-Gaussian amplitude dominated by ε^3 interactions, which leads to a breakdown of perturbation theory on small scales. To address this, the authors propose a weakly-coupled model with a c(φ) that reduces the transition strength after generating observable modes, yielding a finite, perturbatively controlled range of scale-invariant Gaussian perturbations with a mild red tilt on small scales. This modification suppresses small-scale power and quantum backreaction, enabling compatibility with cosmological observations, though at the cost of a somewhat narrower scale-invariant window. The work also outlines future directions, including incorporating a time-dependent sound speed to further tame non-linearities and strong coupling.
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.