The Space-Medium: A Timeless Physical Framework for the Origin, Structure, and Fate of the Universe

This paper reformulates general relativity in a time-free (timeless) framework by treating the universe as a self-consistent spatial medium rather than a four-dimensional spacetime. Starting from the Einstein–Hilbert action, the derivation proceeds through the ADM and Baierlein–Sharp–Wheeler (BSW) formalisms to obtain a Jacobi-type action in which physical time emerges relationally from internal fields. The model interprets gravity, cosmic expansion, and the dark sector as manifestations of a single medium with inertial and elastic modes, characterized by the parameters wE, μ, and Θ. These parameters lead to measurable deviations—such as small gravitational-slip and Integrated Sachs–Wolfe effects—providing a conservative, testable extension of standard general relativity that requires no new forces or constants.