= Einstein static universe
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The Einstein static universe has a time-independent <scale factor> and positively curved spatial sections with the geometry of a round <three-sphere>. For pressureless <matter> and a positive <cosmological constant>, its static conditions in units $c=1$ are $\Lambda=4\pi G\rho$ and $a_E^{-2}=\Lambda$.
The first equality balances matter's attractive contribution in the <Friedmann acceleration equation> against the cosmological repulsion; the second follows from the <Friedmann equation> with zero expansion. Spatial <curvature> enters that constraint, rather than being the attractive source in the acceleration balance. This is an exact equilibrium model. Whether a perturbed model remains near it requires a separate stability analysis.
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