Gravitational collapse of matter in the presence of nonminimally coupled quintessence and phantomlike scalar fields

This paper explores the evolution of the overdense region of dark matter in the presence of a nonminimally coupled scalar field which is used to model quintessence and phantomlike dark energy. We focus on algebraic coupling, where the interaction Lagrangian is independent of the derivatives of the scalar field. To make our model more relativistic, like the minimal coupling scenario we studied earlier, we consider a spacetime structure that is internally closed Friedmann-Lema\^{}tre-Robertson-Walker (FLRW) spacetime and externally the generalized Vaidya spacetime. This structure allows nonzero matter flux at the boundary of the overdense region. Our investigation reveals that an increment of the coupling strength causes dark energy to cluster with dark matter at a certain cosmological scale where the influence of dark energy cannot be ignored. This phenomenon arises from the specific nature of the nonminimal coupling considered in this paper. While the evolution of matter's energy density remains unchanged, the scalar field's Klein-Gordon equation is modified, causing dark energy to deviate from its homogeneous state and cluster with dark matter. Similar to minimal coupling scenarios, closed spherical regions do not collapse within certain parameter ranges, exhibiting eternal expansion within the spatially flat FLRW spacetime and acting as voids with decreasing matter density. The study extends our understanding of the cosmological scenarios where the virialization of the overdense regions of dark matter is influenced by the nonminimally coupled dark energy.