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

The title question is meant literally: we ask whether the expansion endsin a static universe, and derive the expansion history from the velocity of freefall instead of from an expansion of space.}% methods (mandatory){Following R{ichard} F{eynman}'s field-dynamic treatment of gravitation,the expansion is described as an outward free fall, which removes the conflict betweena peculiar velocity of the celestial bodies and a comoving frame. Two elements carrythe argument. The first is the equality of kinetic and gravitational time dilation:the same quantity may be read as a velocity or as a potential, so that the kinetic andthe gravitational view are interchangeable throughout. The second is the vanishing ofthe total energy in free fall. Matter is taken to be baryonic, its dark componentarising through a mass factor q and dark energy through a factor x. Because thetwo dilations agree, q can be written without any motion at all, asq = 1/(1+Φ/c²): the mass factor is a property of the potential.}% results (mandatory){The algorithm is closed by Newton iteration and yields a present cosmic radiusR₀ = 1.2775 · 10²⁶\,m and a total baryonic massM = 3.696 · 10⁵¹\,kg. After the Big Bang the model passes through amaximum of about $111\,%$ of the present size and then contracts towards a staticuniverse of ~ 97\,%, reached after roughly five times the present age.Spacetime is curved: hyperbolic at the Big Bang, briefly spherical, slightlyhyperbolic today; the measured Ωₖ = 0.0007 is an input. The Hubble tension isaddressed by assigning the two measured values to distinct quantities, a geometricHCMB and an observed HDL = c/R. The latter falls from$72.4$ to about 65\,kms · Mpc ata ≈ 0.15 and then rises steeply --- a non-monotonic behaviour thatΛCDM does not show and that a sufficiently deep distance ladder canfalsify.