A Nonsingular Cosmology with a Scale-Invariant Spectrum of Cosmological Perturbations from Lee-Wick Theory

TL;DR

This paper explores a nonsingular bouncing cosmology derived from Lee-Wick scalar fields, demonstrating that quantum vacuum fluctuations can produce a scale-invariant spectrum of cosmological perturbations without requiring inflation.

Contribution

It introduces a Lee-Wick scalar field model that yields nonsingular bounces and shows that quantum vacuum fluctuations naturally generate scale-invariant spectra in this context.

Findings

Nonsingular cosmological bounces are achieved with Lee-Wick fields.

Quantum vacuum fluctuations produce scale-invariant spectra post-bounce.

The model predicts a non-suppressed tensor-to-scalar ratio.

Abstract

We study the cosmology of a Lee-Wick type scalar field theory. First, we consider homogeneous and isotropic background solutions and find that they are nonsingular, leading to cosmological bounces. Next, we analyze the spectrum of cosmological perturbations which result from this model. Unless either the potential of the Lee-Wick theory or the initial conditions are finely tuned, it is impossible to obtain background solutions which have a sufficiently long period of inflation after the bounce. More interestingly, however, we find that in the generic non-inflationary bouncing cosmology, perturbations created from quantum vacuum fluctuations in the contracting phase have the correct form to lead to a scale-invariant spectrum of metric inhomogeneities in the expanding phase. Since the background is non-singular, the evolution of the fluctuations is defined unambiguously through the bounce. We also analyze the evolution of fluctuations which emerge from thermal initial conditions in the contracting phase. The spectrum of gravitational waves stemming for quantum vacuum fluctuations in the contracting phase is also scale-invariant, and the tensor to scalar ratio is not suppressed.