Does the Universe Have a Static Future? A Theoretical Evaluation Based on Free-Fall Expansion and Equivalent Time Dilations

Abstract

We derive the expansion history of the universe from the velocity of freefall. Following Richard Feynman’s field-dynamic treatment of gravitation, theexpansion is described as an outward free fall rather than as an expansion ofspace, which removes the conflict between a peculiar velocity of the celestial bodies and a comoving frame. Two further elements are essential: the equivalence ofkinetic and gravitational time dilation, and the vanishing of the total energy infree fall. Matter is taken to be baryonic throughout, its dark component arisingas relativistic mass through a mass factor q, and dark energy enters through acorresponding factor x.The resulting algorithm is closed by Newton iteration and yields a present cosmicradius R0 = 1.2775 · 1026 m and a total baryonic mass M = 3.696 · 1051kg.After the Big Bang the model passes through a maximum of about 111% of thepresent size and contracts towards a static universe of ∼ 97% of the presentsize, reached after roughly five times the present age. The algorithm requiresa curved spacetime: hyperbolic at the Big Bang, briefly spherical, and slightlyhyperbolic today and in the future. The curvature factor k(a) varies over theexpansion history and vanishes at exactly one epoch, so the universe cannot beflat throughout. The measured curvature parameter Ωk = 0.0007 is adopted asinput, which places that epoch at a = 0.982 rather than at a = 1; the closurecondition k(1) = k0 is then met to the working precision of the computation,as is the zero-energy condition across the entire expansion history.The Hubble tension is addressed by assigning both measured values to distinctquantities within one algorithm: a geometric parameter HCMB and an observedparameter HDL = c/R. The latter is the sharpest prediction of the model. FromHDL = 72.4 km/s·Mpc today it falls to a minimum of ∼ 65 km/s·Mpc at a ≈ 0.15 andthen rises steeply towards the Big Bang (Fig. 5) — a non-monotonic behaviourthat ΛCDM does not exhibit, and one that a sufficiently deep measurement ofthe distance ladder can falsify.