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) = lL(beta) (1 + z)(n), only intermediate-luminosity quasars (10(27) W/Hz < L < 10(28) W/Hz) show negligible dependence (vertical bar n vertical bar similar or equal to 10(-3), vertical bar beta vertical bar similar or equal to 10(-4)),andthus 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(-0.145)(5)(+0.24) and the Hubble constant H-0 = 66.30(-8.5 0)(+7.00) km sec(-1) Mpc(-1). Finally, with the angular diameter distances D-A measured for quasars extending to high redshifts (z similar to 3.0), we reconstruct the DA(z) function using the technique of Gaussian processes. This allows us to identify the redshift corresponding to the maximum of the DA(z) function: z(m) = 1.70 and the corresponding angular diameter distance DA(z(m)) = 1719.01 +/- 43.46 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 +/- 6.11 km sec(-1) Mpc(-1). These measurements are used to estimate the speed of light: c = 3.039(+/- 0.180) x 10(5) km/s. This is the first measurement of the speed of light in a cosmological setting referring to the distant past.