We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct effective equations derived from semiclassical states. We show that requiring a bounce at the Planck density uniquely selects the volume lattice and gives the same effective Friedmann equation as that obtained in loop quantum cosmology. We also present conditions for the validity of the effective equations.

中文翻译：

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量子宇宙学作为盒子中的晶格


我们在度量变量中描述了标量场宇宙学的量化方案，这些变量具有由晶格施加的基本离散性。选择用于量化的变量决定了晶格，每个晶格都会产生从半经典状态派生的不同有效方程。我们表明，在普朗克密度处需要反弹可以唯一地选择体积晶格，并给出与在环量子宇宙学中获得的相同的有效弗里德曼方程。我们还提出了有效方程有效性的条件。