Spacetime Noncommutativity and Antisymmetric Tensor Dynamics in the Early Universe

TL;DR

This paper explores how antisymmetric tensor fields, linked to spacetime noncommutativity at the Planck scale, influence early universe cosmology, leading to anisotropies and isotropization effects in Bianchi I models.

Contribution

It introduces a dynamical antisymmetric tensor field into cosmological models and analyzes its effects on universe evolution, a novel approach to spacetime noncommutativity implications.

Findings

Antisymmetric tensor effects dominate early universe dynamics.

Late-time isotropization driven by scalar field.

Approximate solutions for Hubble parameter evolution.

Abstract

This paper investigates the possible cosmological implications of the presence of an antisymmetric tensor field related to a lack of commutatitivity of spacetime coordinates at the Planck era. For this purpose, such a field is promoted to a dynamical variable, inspired by tensor formalism. By working to quadratic order in the antisymmetric tensor, we study the field equations in a Bianchi I universe in two models: an antisymmetric tensor plus scalar field coupled to gravity, or a cosmological constant and a free massless antisymmetric tensor. In the first scenario, numerical integration shows that, in the very early universe, the effects of the antisymmetric tensor can prevail on the scalar field, while at late times the former approaches zero and the latter drives the isotropization of the universe. In the second model, an approximate solution is obtained of a nonlinear ordinary differential equation which shows how the mean Hubble parameter and the difference between longitudinal and orthogonal Hubble parameter evolve in the early universe.