Geometric Deformation Wave Model of Brane Cosmology: A Unified Origin of Gravitation, Matter, Dark Matter and Dark Energy

Abstract

We introduce a deformation wave model of brane cosmology, where a 5D membrane embedded in a 6D bulk spacetime undergoes intrinsic geometric deformations triggered by a Gaussian perturbation. This process drives a three-stage cosmic evolution—inflation zone, transition, and membrane oscillation—forming a “universe factory” that generates stable 4D universes at wave crests (matter-dominated) and troughs (antimatter-dominated). The Einstein Field Equations (EFE) are derived geometrically from the brane’s elastic dynamics, without invoking traditional inflation-like scalar fields, providing a physical mechanism for spacetime curvature. Dark energy emerges from the membrane’s intrinsic wave speed, yielding a constant density incorporated Λ h μ ν as in the EFE, consistent with late-time acceleration ( Ω Λ = 0.7 ). Dark matter arises as the predecessor universes gravity traces in dark sectors, reproducing galactic ratios ( ρ D M ρ b ≈ 5 ). The model aligns with CMB observations ( n s = 0.96 ) and predicts a finite multiverse with testable CMB anisotropies. This framework unifies gravity, dark matter, and dark energy geometrically, offering a physically grounded alternative to standard brane inflation and ΛCDM.