A Phenomenological Critical-Density Bounce in a Closed FLRW Interior: Interior Dynamics, Curvature, and Constraints on Schwarzschild Matching
Namith Tishan Rathnayake
Abstract
This paper investigates a phenomenological model of a finite-density cosmological bounce within a closed Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. The model modifies the Friedmann equation through a critical-density correction, introducing a density scale at which the Hubble parameter vanishes and a transition from contraction to expansion may occur. Assuming pressureless matter, the analysis derives the minimum scale factor, examines the conditions for a bounce and subsequent recollapse, and evaluates curvature invariants at the bounce to determine whether they remain finite for finite model parameters. The possible application of this framework to black-hole interiors is then considered. However, connecting a closed FLRW interior consistently to a Schwarzschild exterior presents additional constraints, including the matching conditions at the boundary and the effective pressure associated with the modified dynamics. The analysis therefore distinguishes the mathematical properties of the proposed interior model from the unresolved problem of constructing a complete black-hole-to-baby-universe spacetime. The critical-density correction is treated as a phenomenological assumption rather than a result derived from a fundamental theory of quantum gravity. The paper establishes a framework for examining these conditions and identifies the further theoretical work required to determine whether the proposed scenario can represent a physically consistent model.