Noncommutative Coherent States and Quantum Cosmology

Abstract

The set of coherent states for a noncommutative quantum Bianchi I anisotropic cosmology were built to circumvent the absence of a simultaneous set of configuration observables. By extending known methods of path integrals with coherent states to their noncommutative analogues allowed us to obtain the formal expression of the propagator of the theory in terms of the covariant Husimi Q-symbol of the quantum constraint. The analysis of the equations of motion resulting from a steepest descent procedure showed the existence of solutions displaying a minimum value of the volume scaling function which are, in turn, compatible with a physically inspired definition for a bounce. More importantly, a lower bound for the volume at the bounce which incorporates quantum mechanical and noncommutativite contributions was established. The asymptotic analysis of the solutions in the vicinity of the bounce was performed by implementing techniques used in boundary-layer problems. The numerical simulations that confirm our results are also presented.