Natural Inflation from Polymer Quantization

TL;DR

This paper explores a novel polymer quantization approach for a scalar field in early universe cosmology, revealing effects on phase space and potential resembling hybrid natural inflation, but does not resolve the initial singularity.

Contribution

It introduces a new polymer quantization scheme where the scalar field amplitude is not well-defined, differing from previous models and connecting to loop quantum gravity concepts.

Findings

Phase space is compactified in the field amplitude direction.

Effective potential resembles hybrid natural inflation.

The approach does not eliminate the big bang singularity.

Abstract

We study the polymer quantization of a homogeneous massive scalar field in the early universe using a prescription inequivalent to those previously appearing in the literature. Specifically, we assume a Hilbert space for which the scalar field momentum is well defined but its amplitude is not. This is closer in spirit to the quantization scheme of loop quantum gravity, in which no unique configuration operator exists. We show that in the semi-classical approximation, the main effect of this polymer quantization scheme is to compactify the phase space of chaotic inflation in the field amplitude direction. This gives rise to an effective scalar potential closely resembling that of hybrid natural inflation. Unlike polymer schemes in which the scalar field amplitude is well-defined, the semi-classical dynamics involves a past cosmological singularity; i.e., this approach does not mitigate the big bang.