The Elastic Universal Phase Theory (EUPT): A Non-Singular, Frictionless Elastic Continuum Mechanics Model for Cosmological Evolution

We present a novel cosmological framework, The Elastic UniversalPhase Theory (EUPT), which reformulates spacetime as a continuous,perfectly frictionless elastic tensor field operating under dynamic scalingphases. By replacing the abstract, non-interacting vacuum of GeneralRelativity with a physical medium possessing intrinsic volumetric tension(Ts) and phase density (ρs), we successfully eliminate the mathematical necessity of singularities while resolving contemporary observationalcrises.We demonstrate that the fundamental metric of the cosmos can bewritten as a function of a Scale Deformation Tensor, σ(t), yielding acyclical cosmic engine governed by a closed invariant energy potentialUtotal = Ukinetic + Uelastic.Under this formulation, we establish three primary analytical solutions: the resolution of the cosmological constant problem via the mechanical invariance of light speed (c = √︁ Ts/ρs); a predictable mechanicalexplanation for the time-varying dark energy density recently reported bythe Dark Energy Spectroscopic Instrument (DESI); and a non-singular“Big Bounce” mechanism that creates primordial structural anchors, resolving the James Webb Space Telescope (JWST) early massive galaxyparadox.