Classical Universe Arising from Quantum Cosmology

In this paper, we study the classical limit of quantum cosmology by applying the Weyl-Wigner-Groenwold-Moyal formalism of deformation quantization to quantum cosmology of Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with positive spatial curvature and conformally coupled scalar field. The corresponding quantum cosmology is described by the Moyal-Wheeler-DeWitt equation which has an exact solution in Moyal phase space, resulting in Wigner quasiprobability distribution function, peaking over the classical solutions. We showed that for a large value of quantum number $n$, the emerged classical universe is filled with radiation with quantum mechanical origin.