We propose a theoretical framework — Discrete Symplectic Cosmology (DSC) — in which cosmic evolution is modeled as a non-autonomous discrete dynamical system on a Planck-scale lattice Z³ x N, equipped with a symplectic structure. From two assumptions (discrete spacetime and symplectic evolution), we derive: (i) an adiabatic cooling law mu (n) = muc + (alphaF/2) /ln² (n) with the Feigenbaum constant alphaF determining the cooling rate; (ii) an effective Einstein equation G₌ₔ ₍ₔ + Lambda (t) g₌ₔ ₍ₔ = (8 pi G/c⁴) T₌ₔ ₍ₔ where Lambda (t) = Lambdaᵢnfty + (4 dH² / 3c²) / (t² ln² (t/tP) ) and dH = ln2/ln (alphaF) is the attractor Hausdorff dimension; and (iii) a Hubble relaxation law H (t) = Hᵢnfty + beta/ln² (t/tP) with beta < 0 derived (not fitted) from attractor contraction in the extended phase space. We illustrate the framework's observational consequences with mock-data comparisons for fine-structure drift, Hubble-parameter evolution, and laboratory clock constraints. Planck-epoch numerical simulations using a Stormer-Verlet integrator confirm the analytic cooling law over 60 decades of lattice time while preserving the symplectic form to machine precision. The framework makes falsifiable predictions, including an asymptotic Hubble limit Hᵢnfty testable by next-generation BAO surveys.
Liang Wang (Fri,) studied this question.
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