Scale-invariant spectrum of Lee-Wick model in de Sitter spacetime

TL;DR

This paper demonstrates that the Lee-Wick scalar model in de Sitter spacetime produces a truly scale-invariant spectrum across the entire spacetime, unlike the massless scalar which is only scale-invariant in the superhorizon region.

Contribution

It shows that the Lee-Wick scalar theory yields a consistent, scale-invariant spectrum in de Sitter space, extending the understanding of inflationary perturbations.

Findings

Lee-Wick model produces a scale-invariant spectrum in de Sitter.

The spectrum is obtained via Fourier transform and direct power spectrum calculation.

Massless scalar shows scale invariance only in superhorizon region.

Abstract

We obtain a scale-invariant spectrum from the Lee-Wick model in de Sitter spacetime. This model is a fourth-order scalar theory whose mass parameter is determined by $M^2=2H^2$. The Harrison-Zel'dovich scale-invariant spectrum is obtained by Fourier transforming the propagator in position space as well as by computing the power spectrum directly. It shows clearly that the LW scalar theory provides a truly scale-invariant spectrum in whole de Sitter, while the massless scalar propagation in de Sitter shows a scale-invariant spectrum in the superhorizon region only.