A bonafide model of structure formation from gravitational collapse

Abstract 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.