In this paper, we study the classical limit and unitary evolution of quantum cosmology by applying the Weyl–Wigner–Groenewold–Moyal formalism of deformation quantization to quantum cosmology of a homogeneous and isotropic universe with positive spatial curvature and conformally coupled scalar field. The corresponding quantum cosmology (similar to the Schrödinger interpretation in canonical quantization scheme of 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 show that for a large value of the quantum number $n$, the emerged classical universe is filled with radiation with quantum mechanical origin. Also, we introduce a canonical transformation on the scalar field sector of the model such that the conjugate momenta of the new canonical variable appear linearly in the transformed total Hamiltonian. Using this canonical transformation, we show that, it may lead to disentangle the time from the true dynamical variables. We obtain the time-dependent Wigner function for a coherent as well as for squeezed states. We show that the peak of these Wigner functions follows the classical trajectory in the phase space.

在本文中，我们将变形量化的Weyl-Wigner-Groenewold-Moyal形式主义应用于具有正空间曲率和保形耦合标量场的均质各向同性宇宙的量子宇宙学，研究了量子宇宙学的经典极限和统一演化。相应的量子宇宙论（类似于量子宇宙论经典量化方案中的薛定ding解释）由Moyal–Wheeler–DeWitt方程描述，该方程在Moyal相空间中具有精确解，从而产生了Wigner拟拟分布函数，在经典解中达到峰值。我们证明对于较大的量子数值$ñ$，出现的古典宇宙充满了具有量子力学起源的辐射。此外，我们在模型的标量场扇区上引入规范变换，以使新规范变量的共轭矩在变换的总哈密顿量中线性出现。使用这种规范的转换，我们表明，它可能导致时间与真实的动力学变量分离。我们获得了相干态和压缩态随时间的维格纳函数。我们证明了这些维格纳函数的峰值遵循相空间中的经典轨迹。