A bound on the scale of spacetime noncommutativity from the reheating phase after inflation

TL;DR

This paper derives upper bounds on spacetime noncommutativity parameters during early universe epochs, especially reheating after inflation, using a UV/IR relationship in noncommutative gauge theories and considering different thermal system sizes.

Contribution

It introduces a method to constrain spacetime noncommutativity using early universe thermal epochs and explores how system size influences these bounds.

Findings

Upper bounds on noncommutativity parameter during reheating.

Bounds depend on the thermal system's nature and size.

Reheating stage provides the tightest constraints.

Abstract

In an approach to noncommutative gauge theories, where the full noncommutative behavior is delimited by the presence of the UV and IR cutoffs, we consider the possibility of describing a system at a temperature T in a box of size L. Employing a specific form of UV/IR relationship inherent in such an approach of restrictive noncommutativity, we derive, for a given temperature T, an upper bound on the parameter of spacetime noncommutativity Lambda_NC ~ |theta|^{-1/2}. Considering such epochs in the very early universe which are expected to reflect spacetime noncommutativity to a quite degree, like the reheating stage after inflation, or believable pre-inflation radiation-dominated epochs, the best limits on Lambda_NC are obtained. We also demonstrate how the nature and size of the thermal system (for instance, the Hubble distance versus the future event horizon) can affect our bounds.