Quantum initial conditions for curved inflating universes

TL;DR

This paper develops a new method for setting initial conditions in curved inflationary universes, enabling canonical quantization and potentially affecting observable primordial power spectra.

Contribution

It introduces a novel curvature perturbation that is canonically normalized and invariant under transformations, resolving longstanding issues in curved cosmology quantization.

Findings

Constructed a unique curvature perturbation normalized in its equation of motion

Enabled invariant initial condition setting under canonical transformations

Identified potential observational effects on the primordial power spectrum

Abstract

We discuss the challenges of motivating, constructing, and quantizing a canonically normalized inflationary perturbation in spatially curved universes. We show that this has historically proved challenging due to the interaction of nonadiabaticity with spatial curvature. We construct a novel curvature perturbation that is canonically normalized in the sense of its equation of motion and is unique up to a single scalar parameter. With this construction it becomes possible to set initial conditions invariant under canonical transformations, overcoming known ambiguities in the literature. This corrected quantization has potentially observational consequences via modifications to the primordial power spectrum at large angular scales, as well as theoretical implications for quantization procedures in curved cosmologies filled with a scalar field.