The quantum state of the universe from deformation quantization and classical-quantum correlation

Abstract

In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl-WignerGroenewold-Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is described by the Moyal-Wheeler-DeWitt equation which has exact solutions in Moyal phase space, resulting in Wigner quasiprobability distribution functions peaking around the classical paths for large values of scale factor. We show that the Wigner functions of these models are peaked around the non-singular universes with quantum modified density parameter of radiation.

Accelerating cosmologies in an integrable model with noncommutative minisuperspace variables

“…The application of the Wigner function has been considered already in quantum cosmologies with deformed phase spaces with slightly different motivations from ours [41,42]. Our present aim is to construct the probability distribution whose arguments are noncommutative variables, say, X and Y , from the Wigner function defined by the wave function of commutative variables x and y.…”