Analytical approximations for curved primordial power spectra

TL;DR

This paper develops analytical approximations for primordial power spectra in inflationary models with spatial curvature, providing insights into how curvature influences observable features like cut-offs and oscillations.

Contribution

It introduces curvature-dependent analytical templates that are potential tools for interpreting cosmological data, independent of specific inflationary potentials.

Findings

Analytical templates match numerical calculations for curved inflationary models.

Curvature effects cause shifts in wavevectors, affecting power spectrum features.

The work generalizes previous models to include spatial curvature effects.

Abstract

We extend the work of Contaldi et al. and derive analytical approximations for primordial power spectra arising from models of inflation which include primordial spatial curvature. These analytical templates are independent of any specific inflationary potential and therefore illustrate and provide insight into the generic effects and predictions of primordial curvature, manifesting as cut-offs and oscillations at low multipoles and agreeing with numerical calculations. We identify through our analytical approximation that the effects of curvature can be mathematically attributed to shifts in the wavevectors participating dynamically.