The model of a multiverse is advanced, which endows subuniverses like ours with space and time and imparts to their matter all information about the physical laws. It expands driven by dark energy (DE), which is felt in our Universe (U) by mass input and expansion–acceleration. This dark multiverse (DM) owes its origin to a creatio ex nihilo, described in previous work by a tunneling process in quasi-classical approximation. Here, this origin is treated again in the context of quantum gravity (QG) by solving a Wheeler de Witt (WdW) equation. Different than usual, the minisuperspace employed is not spanned by the expansion parameter a but by the volume 2 π 2 a 3 . This not only modifies the WdW-equation, but also probabilities and solution properties. A “soft entry” can serve the same purpose as a tunneling process. Sections of solutions are identified, which show qualitative features of a volume-quantisation, albeit without a stringent quantitative definition. A timeless, spatially four-dimensional primordial state is also treated, modifying a state proposed by Hartle and Hawking (HH). For the later classical evolution, elaborated in earlier papers, a wave function is calculated and linked to the solutions for the quantum regime (QR). It is interpreted to mean that the expansion of the DM proceeds in submicroscopic leaps. Further results are also derived for the classical solutions.
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机译：多元宇宙的模型是先进的，它赋予像我们这样的子宇宙以时空的方式，并将有关物理定律的所有信息赋予它们。它是由暗能量（DE）驱动的，它通过质量输入和膨胀-加速在我们的宇宙（U）中感受到。这种黑暗的多元宇宙（DM）起源于无创的创造，在先前的工作中通过准经典近似的隧穿过程对其进行了描述。在此，通过解算Wheeler de Witt（WdW）方程，再次在量子引力（QG）的情况下处理此原点。与通常不同，所采用的超微空间不是由扩展参数a跨越，而是由体积2π2 a 3跨越。这不仅修改了WdW方程，而且还修改了概率和解属性。 “软条目”可以起到与隧道过程相同的作用。确定了解决方案的各个部分，尽管没有严格的定量定义，但这些部分显示了体积量化的定性特征。还处理了永恒的空间四维原始状态，修改了Hartle and Hawking（HH）提出的状态。对于早期论文中阐述的后来的经典进化，计算了波动函数并将其与量子态（QR）的解联系起来。这被解释为意味着DM的膨胀以亚微观跃迁进行。对于经典解还得出了进一步的结果。
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