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arXiv · 2103.15424

Spherical space in the Newtonian limit: The cosmological constant

J. M. Isidro·P. Fernandez de Cordoba·J. C. Castro-Palacio
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Abstract

We compute the cosmological constant of a spherical space in the limit of weak gravity. To this end we use a duality developed by the present authors in a previous work. This duality allows one to treat the Newtonian cosmological fluid as the probability fluid of a single particle in nonrelativistic quantum mechanics. We apply this duality to the case when the spacetime manifold on which this quantum mechanics is defined is given by $\mathbb{R}\times\mathbb{S}^3$. Here $\mathbb{R}$ stands for the time axis and $\mathbb{S}^3$ is a 3-dimensional sphere endowed with the standard round metric. A quantum operator $\Lambda$ satisfying all the requirements of a cosmological constant is identified, and the matrix representing $\Lambda$ within the Hilbert space $L^2\left(\mathbb{S}^3\right)$ of quantum states is obtained. Numerical values for the expectation value of the operator $\Lambda$ in certain quantum states are obtained, that are in good agreement with the experimentally measured cosmological constant.

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J. M. Isidro, P. Fernandez de Cordoba, J. C. Castro-Palacio. 2021-03-29. Spherical space in the Newtonian limit: The cosmological constant. https://doi.org/10.1142/s0218271821500838

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