Membrane Curvature Theory — Revised Candidate Mathematical Framework

Abstract

This preprint presents the revised candidate mathematical framework for the Dark Matter Energy Theory (DMET), a speculative gravity-first cosmological model exploring whether effects attributed to dark matter and dark energy could arise from spacetime geometry rather than separate unknown substances. The paper extends the shorter weak-field formulation into a broader relativistic research programme. It includes a nonlinear galaxy-scale gravity model, candidate five-dimensional and brane-inspired equations, gravitational lensing requirements, large-scale tidal curvature, geodesic deviation, the Raychaudhuri equation, effective stress/curvature contributions to cosmic acceleration, directional expansion, early-universe structure considerations, and explicit observational failure criteria. A separate speculative section develops the neighbouring-region/JWST extension. It distinguishes gravitational lensing from cross-region geometrical redshift and considers photon propagation, coherent spectral redshift, time-dilation behaviour, flux, magnification, and possible transfer across an inter-region boundary. The framework is exploratory and is not presented as a complete or validated replacement for General Relativity or ΛCDM. Its purpose is to identify the mathematical structures, consistency requirements, observations, and falsification tests that would be needed to determine whether the underlying DMET concept is physically viable.