Measuring the Hubble constant through the galaxy pairwise peculiar velocity

The Hubble constant $H_0$, the current expansion rate of the universe, is one of the most important parameters in cosmology. The cosmic expansion regulates the mutually approaching motion of a pair of celestial objects due to their gravity. Therefore, the mean pairwise peculiar velocity of celestial objects, which quantifies their relative motion, is sensitive to both $H_0$ and the dimensionless total matter density ${\mathrm{\Omega }}_m$. Based on this, using the Cosmicflows-4 data, we measured $H_0$ for the first time via the galaxy pairwise velocity in the nonlinear and quasi-linear range. Our results yield $H_0=75.5\pm 1.4$ km s${}^{-1}$ Mpc${}^{-1}$ and ${\mathrm{\Omega }}_m=0.311_{-0.028}^{+0.029}$ . The uncertainties of $H_0$ and ${\mathrm{\Omega }}_m$ can be improved to around 0.6% and 2%, respectively, if the statistical errors become negligible in the future.