Measuring the speed of light with ultra-compact radio quasars

In this paper, based on a 2.29 GHz VLBI all-sky survey of 613 milliarcsecond ultra-compact radio sources with $0.0035<z<3.787$, we describe a method of identifying the sub-sample which can serve as individual standard rulers in cosmology. If the linear size of the compact structure is assumed to depend on source luminosity and redshift as $l_m=l L^\beta (1+z)^n$, only intermediate-luminosity quasars ($10^{27}$ W/Hz$<L<$ $10^{28}$ W/Hz) show negligible dependence ($|n|\simeq 10^{-3}$, $|\beta|\simeq 10^{-4}$), and thus represent a population of such rulers with fixed characteristic length $l=11.42$ pc. With a sample of 120 such sources covering the redshift range $0.46<z<2.80$, we confirm the existence of dark energy in the Universe with high significance under the assumption of a flat universe, and obtain stringent constraints on both the matter density $\Omega_m=0.323^{+0.245}_{-0.145}$ and the Hubble constant $H_0=66.30^{+7.00}_{-8.50}$ km sec$^{-1}$ Mpc$^{-1}$. Finally, with the angular diameter distances $D_A$ measured for quasars extending to high redshifts ($z\sim 3.0$), we reconstruct the $D_A(z)$ function using the technique of Gaussian processes. This allows us to identify the redshift corresponding to the maximum of the $D_A(z)$ function: $z_m=1.70$ and the corresponding angular diameter distance $D_A(z_m)=1719.01\pm43.46$ Mpc. Similar reconstruction of the expansion rate function $H(z)$ based on the data from cosmic chronometers and BAO gives us $H(z_m)=176.77\pm6.11$ km sec$^{-1}$ Mpc$^{-1}$. These measurements are used to estimate the speed of light: $c=3.039(\pm0.180)\times 10^5$ km/s. This is the first measurement of the speed of light in a cosmological setting referring to the distant past.