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 [Formula: see text]. Here, [Formula: see text] stands for the time axis and [Formula: see text] is a 3-dimensional sphere endowed with the standard round metric. A quantum operator [Formula: see text] satisfying all the requirements of a cosmological constant is identified, and the matrix representing [Formula: see text] within the Hilbert space [Formula: see text] of quantum states is obtained. Numerical values for the expectation value of the operator [Formula: see text] in certain quantum states are obtained, which are in good agreement with the experimentally measured cosmological constant.