Duality Invariance of Cosmological Perturbation Spectra

TL;DR

This paper demonstrates that cosmological perturbation spectra from quantum fluctuations are invariant under certain background transformations, linking different inflationary and collapsing universe models producing similar spectra.

Contribution

It introduces a duality symmetry in cosmological perturbation spectra, connecting diverse background evolutions that yield identical observational signatures.

Findings

Spectra are invariant under a two-parameter family of background transformations.

Scale-invariant spectra can arise from both exponential expansion and collapsing universe models.

Duality relates slow-roll inflation to non-slow-roll solutions.

Abstract

I show that cosmological perturbation spectra produced from quantum fluctuations in massless or self-interacting scalar fields during an inflationary era remain invariant under a two parameter family of transformations of the homogeneous background fields. This relates slow-roll inflation models to solutions which may be far from the usual slow-roll limit. For example, a scale-invariant spectrum of perturbations in a minimally coupled, massless field can be produced by an exponential expansion with $a\propto e^{Ht}$, or by a collapsing universe with $a\propto (-t)^{2/3}$.