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\textsc{ichard} F\textsc{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, as$q = 1/(1+\Phi/c^2)$: the mass factor is a property of the potential.}% results (mandatory){The algorithm is closed by Newton iteration and yields a present cosmic radius$R_0 = 1.2775 \cdot 10^{26}\,\text{m}$ and a total baryonic mass$M = 3.696 \cdot 10^{51}\,\text{kg}$. After the Big Bang the model passes through amaximum of about $111\,\%$ of the present size and then contracts towards a staticuniverse of $\sim 97\,\%$, reached after roughly five times the present age.Spacetime is curved: hyperbolic at the Big Bang, briefly spherical, slightlyhyperbolic today; the measured $\Omega_k = 0.0007$ is an input. The Hubble tension isaddressed by assigning the two measured values to distinct quantities, a geometric$H_{\text{CMB}}$ and an observed $H_{\text{DL}} = c/R$. The latter falls from$72.4$ to about $65\,\frac{\text{km}}{{\text{s}} \cdot {\text{Mpc}}}$ at$a \approx 0.15$ and then rises steeply --- a non-monotonic behaviour that$\Lambda$CDM does not show and that a sufficiently deep distance ladder canfalsify.