Dynamics of Inflationary Universes with Positive Spatial Curvature

TL;DR

This paper investigates how positive spatial curvature influences inflationary universe models, revealing that curvature dominates early inflation, constrains e-foldings, and depends on current density and inflation end time.

Contribution

It introduces a multi-stage model to quantify limits on inflationary e-foldings considering positive curvature effects.

Findings

Curvature dominates early inflation in positively curved universes.

Limits on e-foldings depend on present density parameter and inflation end epoch.

Curvature effects are independent of pre-inflationary conditions.

Abstract

If the spatial curvature of the universe is positive, then the curvature term will always dominate at early enough times in a slow-rolling inflationary epoch. This enhances inflationary effects and hence puts limits on the possible number of e-foldings that can have occurred, independently of what happened before inflation began and in particular without regard for what may have happened in the Planck era. We use a simple multi-stage model to examine this limit as a function of the present density parameter $\Omega_0$ and the epoch when inflation ends.