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The $H_0$-tension problem poses a confrontation of dark energy drivinglate-time cosmological expansion measured by the Hubble parameter $H(z)$ overan extended range of redshifts $z$. Distinct values $H_0\simeq 73$km\,s$^{-1}$Mpc$^{-1}$ and $H_0\simeq 68$ km\,s$^{-1}$Mpc$^{-1}$ obtain fromsurveys of the Local Universe and, respectively, $\Lambda$CBM analysis of theCMB. These are representative of accelerated expansion with$H^\prime(0)\simeq0$ by $\Lambda=\omega_0^2$ and, respectively, $H^\prime(0)>0$in $\Lambda$CDM, where $\omega_0=\sqrt{1-q}H$ is a fundamental frequency of thecosmological horizon in a Friedmann-Robertson-Walker universe with decelerationparameter $q(z)=-1+(1+z)H^{-1}H^\prime(z)$. Explicit solutions$H(z)=H_0\sqrt{1+\omega_m(6z+12z^2+12z^3+6z^4+(6/5)z^5)}$ and, respectively,$H(z)=H_0\sqrt{1-\omega_m+\omega_m(1+z)^3}$ are here compared with recent dataon $H(z)$ over $0\lesssim z \lesssim2$. The first is found to be free oftension with $H_0$ from local surveys, while the latter is disfavored at$2.7\sigma$. A further confrontation obtains in galaxy dynamics by a finitesensitivity of inertia to background cosmology in weak gravity, putting anupper bound of $m\lesssim 10^{-30}$eV on the mass of dark matter. A $C^0$ onsetto weak gravity at the de Sitter scale of acceleration $a_{dS}=cH(z)$, where$c$ denotes the velocity of light, can be seen in galaxy rotation curvescovering $0\lesssim z \lesssim 2$. Weak gravity in galaxy dynamics herebyprovides a proxy for cosmological evolution.

Accelerated cosmological expansion without tension in the Hubble parameter