We present a simple quantum-mechanical estimate of the cosmological constant of a Newtonian Universe. We first mimic the dynamics of a Newtonian spacetime by means of a nonrelativistic quantum mechanics for the matter contents of the Universe (baryonic and dark) within a fixed (i.e. nondynamical) Euclidean spacetime. Then we identify an operator that plays, on the matter states, a role analogous to that played by the cosmological constant. Finally, we prove that there exists a quantum state for the matter fields, in which the above-mentioned operator has an expectation value equal to the cosmological constant of the given Newtonian Universe.

中文翻译：

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牛顿近似中的涌现时空宇宙常数

我们对牛顿宇宙的宇宙常数进行了简单的量子力学估计。我们首先通过非相对论量子力学模拟牛顿时空的动力学，用于固定（即非动力学）欧几里得时空中的宇宙物质（重子和暗）。然后我们确定了一个算子，它在物质状态上所起的作用类似于宇宙常数所起的作用。最后，我们证明了物质场存在一个量子态，其中上述算子的期望值等于给定牛顿宇宙的宇宙学常数。