Gravitational collapse of Matter in the presence of Scalar field Dark energy

This study examines the gravitational collapse of an overdense dark matter region in a coupled scalar field dark energy scenario within a flat FLRW background. It finds that, depending on the initial conditions, some overdense regions avoid collapse and expand eternally with the background. The interior overdense region follows a closed FLRW metric, while its boundary is described by generalized Vaidya spacetime, which allows flux across the boundary while preserving the homogeneity of dark energy inside. Dark matter evolves as cold dark matter, but in non-minimal coupling, the modified Klein-Gordon equation alters dark energy evolution. The results highlight the impact of coupled dark energy on dark matter virialization and cosmic structure formation.

💡 Research Summary

This paper investigates how a scalar‑field dark energy component, either quintessence or phantom, influences the gravitational collapse of an overdense dark‑matter region embedded in an otherwise flat Friedmann‑Lemaître‑Robertson‑Walker (FLRW) universe. The authors construct a two‑zone model: the interior overdensity is described by a closed FLRW metric (k = 1) while the exterior is the standard flat FLRW background (k = 0). The boundary between the two regions is modeled with a generalized Vaidya spacetime, which permits a radial flux of matter and energy across the surface while keeping the dark‑energy density homogeneous inside the collapsing region.

Starting from a covariant action that includes the Einstein–Hilbert term, a perfect‑fluid dark‑matter sector, a canonical scalar field (\phi) with kinetic sign (\epsilon=\pm1) (plus sign for quintessence, minus for phantom), a potential (V(\phi)), and an interaction term (\rho_{\rm int}(n,s,\phi)) coupling matter density (n) and the scalar, the authors derive the Einstein equations and the modified Klein‑Gordon equation. In the minimal‑coupling limit (\rho_{\rm int}=0) the scalar evolves independently; in the non‑minimal case the interaction modifies both the dark‑matter continuity equation and the scalar dynamics.

The interior Friedmann equations become \