Power spectrum for perturbations in an inflationary model for a closed universe

TL;DR

This paper derives the primordial power spectrum for a closed inflationary universe, revealing a large-scale power deficit compared to flat models, using a quantum gravity approach with gauge-invariant variables.

Contribution

It introduces a novel derivation of the power spectrum in a closed universe using a Born--Oppenheimer approximation from the Wheeler--DeWitt equation.

Findings

Closed universe shows a large-scale power deficit.

Method employs gauge-invariant variables in quantum gravity.

Provides insights into curvature effects on primordial fluctuations.

Abstract

We derive the power spectrum of primordial quantum fluctuations in an inflationary universe for curvature parameter ${\mathcal K}=1$. This is achieved through a Born--Oppenheimer type of approximation scheme from the Wheeler--DeWitt equation of canonical quantum gravity using gauge-invariant variables. Compared to the flat model, the closed model exhibits a deficit of power at large scales.