Milliarcsecond compact structure in radio quasars and the geometry of the universe

In this paper, by using the recently compiled set of 120 intermediate-luminosity quasars (ILQSO) observed in a single-frequency VLBI survey, we propose an improved model-independent method to probe cosmic curvature parameter ${\mathrm{\Omega }}_k$ and make the first measurement of the cosmic curvature referring to a distant past, with redshifts up to $z\sim 3.0$. Compared with other methods, the proposed one involving the quasar data achieves constraints with higher precision in this redshift range. More importantly, our results indicate that the measured ${\mathrm{\Omega }}_k$ is in good agreement with zero cosmic curvature, implying that there is no significant deviation from a flat Universe. Finally, we investigate the possibility of testing ${\mathrm{\Omega }}_k$ with a much higher accuracy using quasars observed in the future VLBI surveys. It is shown that our method could provide a reliable and tight constraint on the prior ${\mathrm{\Omega }}_k$ and one can expect the zero cosmic curvature to be established at the precision of $\mathrm{\Delta }{\mathrm{\Omega }}_k\sim {10}^{-2}$ with 250 well-observed radio quasars.