  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.
