Reconciling dark cosmology by duality in the Friedmann scale factor

We report on a duality $D(a)+D(\kappa)=2$ satisfied by the Friedmann scale factor $a$ with curvature $\kappa=1/a$ in terms of the nondimensional operator $D(u)=\ddot{u}u/\dot{u}^2$. The Hubble parameter hereby satisfies $H(z)=H_0\sqrt{1+A(z)}/(1+z)$, where $A(z)$ is a polynomial in the normalized densities of radiation, matter and curvature at redshift $z=0$. Late-time three-flat cosmology satisfies $D(\kappa)=3\Omega_M$. With no free parameters, it alleviates $H_0$-tension between $\Lambda$CDM and the Local Distance Ladder consistent with the age of the Universe based on globular clusters. The mass of the associated dark matter particle is herein bounded by $8.8\times 10^{-24}$eV by what appears to be $C^0$-galaxy dynamics in SPARC galaxy rotation curves. (Based on van Putten, 2020, MNRAS, 491, L6.)