A natural model for curved inflation

TL;DR

This paper introduces a universal curved inflation model within a modified gravity framework, allowing standard quantization methods and providing a natural solution for inflation in curved universes without extra parameters.

Contribution

It proposes a simple, universal curved inflation model using a topological modification of gravity that applies to any background curvature without extra assumptions.

Findings

Model is applicable to any background curvature.

Uses standard quantization and Bunch-Davies vacuum.

Provides a natural solution to curved inflation construction.

Abstract

Inflationary models with a non-zero background curvature require additional hypothesis or parameters compared to flat inflation and the procedure to construct them cannot be as simple as in the flat case. For this reason, there is no consensus on the primordial power spectrum that should be considered at large scales in a curved Universe. In this letter, we propose a model of curved inflation in which the usual canonical quantization and Bunch-Davies vacuum choice of the flat case can be considered. The framework is a recently proposed modification of general relativity in which a non-dynamical topological term is added to the Einstein equation. The model is universal as it is the same for any background curvature, and no additional parameters or hypothesis on the initial spatial curvature are introduced. This gives a natural and simple solution to the problem of constructing curved inflation, and at the same time provides an additional argument for this topological modification of general relativity.