# Primordial power spectra for curved inflating universes

## TL;DR

This paper computes exact primordial power spectra for curved universes using Planck 2018 data, revealing features like cut-offs and oscillations that improve data fit and discussing theoretical implications for initial conditions in curved inflation.

## Contribution

It provides the first detailed numerical computation of primordial spectra for curved universes and analyzes their observational and theoretical implications.

## Key findings

- Spectra exhibit cut-offs and oscillations within observable range.
- Curved universe models fit current CMB data better than flat models.
- Derivations of Mukhanov-Sasaki equation for curved backgrounds are presented.

## Abstract

Exact numerical primordial primordial power spectra are computed and plotted for the for the best-fit Planck 2018 curved universe parameters. It is found that the spectra have generic cut-offs and oscillations within the observable window for the level of curvature allowed by current CMB measurements and provide a better fit to current data. Derivations for the Mukhanov-Sasaki equation for curved universes are presented and analysed, and theoretical implications for the quantum and classical initial conditions for inflation are discussed within the curved regime.