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Theoretical study demonstrates cosmic expansion and collapse via higher-dimensional geometry, indicating an impending Big Crunch and gravitational echoes.
We propose a geometric alternative to the standard cosmological model. The Big Bang and Big Crunch are interpreted as the emergence and disappearance of the overlap region between a 4D hypersphere and a 3D hypersurface moving through it at constant velocity. The model depends on only two geometric parameters: the hypersphere radius RR and the sweep velocity vv. The scale factor is derived as a(τ)=2Rvτ−v2τ2a(τ)=2Rvτ−v2τ2. From this single expression, the Hubble parameter, deceleration parameter, curvature evolution, and effective dark energy density are all obtained without additional free parameters. The model reproduces the radiation-dominated epoch a∝t1/2a∝t1/2, the near-flatness of the present universe, and the observed values of the fine-structure constant and dark matter abundance. It predicts a definitive Big Crunch at τ=2R/vτ=2R/v, a time-varying equation of state for dark energy, and discrete gravitational wave echoes in the 0.01-0.1 Hz band.
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CY Ma (2026) studied this question.
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