Quantum initial conditions for curved inflating universes

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.

15 pages, 3 figures; v3: As published in PRD

References in corpus (18)

• Planck evidence for a closed Universe and a possible crisis for cosmology
• Eppur è piatto? The cosmic chronometer take on spatial curvature and cosmic concordance
• The galaxy power spectrum take on spatial curvature and cosmic concordance
• Just enough inflation: power spectrum modifications at large scales
• Preferred instantaneous vacuum for linear scalar fields in cosmological space-times
• Full-Shape Galaxy Power Spectra and the Curvature Tension
• CMB quadrupole suppression: I. Initial conditions of inflationary perturbations
• The CMB Quadrupole depression produced by early fast-roll inflation: MCMC analysis of WMAP and SDSS data
• A classical bounce: constraints and consequences
• CMB quadrupole suppression: II. The early fast roll stage
• Cosmological constraints on slow-roll inflation: an update
• A note on perfect scalar fields
• Novel quantum initial conditions for inflation
• Power spectrum for perturbations in an inflationary model for a closed universe
• ${\varphi }^4$ inflation is not excluded
• Imprint of spatial curvature on inflation power spectrum
• Primordial power spectra from $k$-inflation with curvature
• Novel vacuum conditions in inflationary collapse models

Cited by in corpus (3)

• Investigating the Origin of CMB Large-Scale Features Using LiteBIRD and CMB-S4
• Time-reversed Stochastic Inflation
• Geodesically Complete Curvature-Bounce Inflation