  This paper explores the cosmological implications of a scalar field with a
specific potential, crucial for achieving the final equilibrium state of
gravitational collapse. We consider a system with two fluids: minimally coupled
matter representing dust-like dark matter and a scalar field acting as dark
energy. Our model, akin to the top-hat collapse model, focuses on isolated
over-dense regions within a closed FLRW metric, while the background follows a
flat FLRW metric. We analyze spacetime configurations where these regions
undergo initial expansion followed by contraction, deriving the scalar field
potential responsible for their equilibrium state. Our fully relativistic
approach offers a comprehensive understanding of stable cosmic over-dense
regions, without the need for ad-hoc Newtonian virialization.
