Chaotic Medium Cosmology I: Foundations of Non-Singular Spacetime from a Structured Medium

We introduce the foundational framework of Chaotic Medium Cosmology (CMC), whichreinterprets spacetime as a structured, chaotic medium rather than an empty geometricmanifold. This first installment develops a modified gravity theory where singularities areavoided through the medium’s finite compressibility. We derive a regular black hole metricbased on a Hayward-type mass function, which eliminates the central singularity whileexactly recovering the Schwarzschild solution asymptotically. The regularization scale ℓrepresents the medium’s structural limit and connects naturally to quantum gravity. Wecompute curvature invariants, horizon structure, and thermodynamic properties, providingtestable predictions for black hole shadows and gravitational waves. This work establishesthe theoretical basis for the screened elasticity model developed in CMC II.