We introduce in this paper a tomographic analysis of the properties of a Friedmann–Lemaitre–Robertson–Walker (FLRW) universe with a perfect fluid. We first review previous works where the Schutz’s parametrization in terms of Clebsch potentials was adopted to describe the perfect fluid. This approach allows to introduce a fiducial time in the Wheeler–De Witt equation. We revisit the properties of the perfect fluid and the introduced Clebsch potentials. In particular, we see that thermasy plays an extremely important role in the definition of fiducial time. The definition of a time and the condition $a\ge 0$ for the expansion factor imply that the Hamiltonian operator must be self-adjoint which implies a restriction on the initial conditions for the wave packet. We show that these allow to obtain well-defined tomograms. Tomograms are marginal functions which incorporate all the information contained in the wave function of the universe, but have the properties of classical probability functions. They can be defined for classical distributions on the phase space as well, enabling us to describe quantum and classical states with the same family of functions. The aim of this paper is to compare the difference between classical tomograms where the Hawking and Penrose theorems imply the inevitability of an initial singular state and the well-defined initial quantum states found in literature. Finally the introduction of a time in the Wheeler–DeWitt allows us to consider the evolution of the classical and quantum initial states of the universe which can be accomplished by introducing a transition probability function for tomograms.

我们在本文中介绍了具有理想流体的 Friedmann-Lemaitre-Robertson-Walker (FLRW) 宇宙的属性的断层扫描分析。我们首先回顾以前的工作，其中采用 Clebsch 势的 Schutz 参数化来描述完美流体。这种方法允许在 Wheeler–De Witt 方程中引入基准时间。我们重新审视完美流体的性质和引入的 Clebsch 势。特别是，我们看到热疗在基准时间的定义中起着极其重要的作用。时间和条件的定义$\mathrm{一个}\ge 0$因为扩展因子意味着哈密顿算子必须是自伴随的，这意味着对波包初始条件的限制。我们表明，这些允许获得明确定义的断层扫描图。Tomograms 是边缘函数，它结合了宇宙波函数中包含的所有信息，但具有经典概率函数的属性。它们也可以定义为相空间上的经典分布，使我们能够用相同的函数族来描述量子态和经典态。本文的目的是比较经典层析成像之间的差异，其中霍金和彭罗斯定理暗示初始奇异状态的必然性与文献中明确定义的初始量子态。