Classical and quantum bicosmology with noncommutativity

TL;DR

This paper explores classical and quantum solutions in a noncommutative bicosmology model, analyzing exact classical solutions, the effects of noncommutativity at small scales, and the quantum Wheeler-DeWitt equation.

Contribution

It revisits a noncommutative bicosmology model, providing exact classical solutions and analyzing quantum behavior with a focus on noncommutativity effects.

Findings

Exact classical solutions with constant noncommutativity are derived.

Noncommutativity influences the behavior of solutions at small scale factors.

The Wheeler-DeWitt equation is formulated and analyzed in the noncommutative context.

Abstract

Recently, Falomir, Gamboa, Mendez, Gondolo and Maldonado proposed a bicosmology scenario [1-4] for solving some cosmological problems related to inflation, dark matter, and thermal history of the universe. Their plan is to introduce noncommutativity into the momentum space of the two scale factors. In the present paper, we revisit their model and first consider exact classical solutions in the model with constant noncommutativity between dynamical variables and between canonical momenta. We also hypothesize that the noncommutativity appears when the scale factors are small, and show the behavior of the classical solution in that case with momentum-space noncommutativity. Finally, we write down the Wheeler-DeWitt equation in that case and examine the behavior of the solution.