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

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.