Post-Shell-Crossing Void Re-expansion (PSC-VR): A Research Compendium

Post-Shell-Crossing Void Re-expansion (PSC-VR): A Research Compendium This archive contains the complete theoretical development of the Post-Shell-Crossing Void Re-expansion (PSC-VR) model, an alternative formation pathway for large cosmic voids within standard General Relativity and collisionless matter dynamics. The PSC-VR framework proposes that a subset of exceptionally large cosmic voids may originate from regions that initially undergo gravitational compression, experience shell-crossing, and subsequently re-expand due to residual kinetic energy and velocity-dispersion support generated during multi-streaming. Unlike standard void formation models based solely on the expansion of primordial underdensities, PSC-VR explores a collapse-and-rebound mechanism driven entirely by known gravitational physics, without invoking exotic matter, modified gravity, or external energy injection. The compendium presents a self-consistent mathematical formulation based on the Lemaître–Tolman–Bondi (LTB) metric for the single-stream phase, explicitly identifies the breakdown of LTB at shell-crossing, and introduces a phenomenological extension motivated by the Vlasov (collisionless Boltzmann) description to model post-crossing dynamics. Clear distinctions are made between established results, phenomenological assumptions, and speculative conjectures. Contents Conceptual motivation and physical picture of PSC-VR Full LTB formulation and collapse dynamics Shell-crossing definition and transition to multi-stream regime Phenomenological velocity-dispersion closure and rebound conditions Energetic consistency analysis Predictions for void sizes, density profiles, velocity fields, and redshift evolution Proposed observational tests (void catalogs, velocity surveys, ISW, lensing) Explicit limitations, uncertainties, and falsifiability criteria Reproducibility guidelines and numerical implementation outline Scope and Status This work is theoretical and exploratory. While the mechanism is physically motivated and energetically plausible, it has not yet been validated by dedicated N-body or Vlasov simulations. The model is therefore presented as a testable hypothesis rather than an established explanation for cosmic voids. PSC-VR is intended as a complementary formation channel to standard void evolution, potentially applicable to a subset of large and supervoid-scale structures in specific cosmic environments.