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This deposit contains the Python verification code accompanying the manuscript "Ensemble Cosmology: A Covariant Framework for Simultaneous Expansion and Collapse".

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Zenodo2026-07-23 更新2026-08-02 收录
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Abstract We develop a covariant variational framework for Ensemble Cosmology, in which the observable universe is treated as one member of a finite collection of interacting Friedmann–Lemaître–Robertson–Walker (FLRW) universes. The framework introduces the Ensemble Scale Factor, defined as the geometric mean of the individual scale factors, the Ensemble Hubble Parameter, and a Shared Ensemble Time Coordinate that describes the collective evolution of the Ensemble while preserving the local Einstein dynamics of every individual universe. Beginning from a unified covariant action, we derive the Ensemble Einstein, Friedmann, Continuity, and Acceleration Equations. The resulting interaction terms satisfy the contracted Bianchi identities and ensure conservation at the Ensemble level without modifying the local gravitational dynamics of the constituent FLRW universes. Cyclic behavior emerges as a collective property of the Ensemble rather than requiring every universe to undergo identical expansion and collapse histories. The formalism is valid for arbitrary finite Ensemble size. A canonical N = 12 Reference Model, motivated by the cuboctahedral kissing-number geometry, is presented as a geometrically symmetric realization of the theory. Its simultaneous expanding and collapsing sectors provide a useful framework for exploring possible observational consequences. The principal analytical results have been independently verified using publicly archived computational software. The framework is compared with Penrose's Conformal Cyclic Cosmology and suggests observational tests involving the cosmic microwave background, baryon acoustic oscillations, DESI, Euclid, the Nancy Grace Roman Space Telescope, the James Webb Space Telescope, and future numerical investigations of the coupled Ensemble equations. Top of Form Bottom of Form

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2026-07-17
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