Spherical space in the Newtonian limit: The cosmological constant

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.

16 pp; clarifications added

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Cited by in corpus (1)

• Hyperbolic space in the Newtonian limit: the cosmological constant