Measuring the speed of light with ultra-compact radio quasars

Abstract

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