Dark energy and the angular size - redshift diagram for milliarcsecond radio sources

Abstract

We investigate observational constraints on the cosmic equation of state from measurements of angular size for a large sample of milliarcsecond compact radio sources. The results are based on a flat Friedmann-Robertson-Walker (FRW) type models driven by non-relativistic matter plus a smooth dark energy component parametrized by its equation of state $p_x = \omega \rho_x$ ($-1 \leq \omega < 0$). The allowed intervals for $\omega$ and $\Omega_{\rm{m}}$ are heavily dependent on the value of the mean projected linear size $l$. For $l \simeq 20h^{-1} - 30h^{-1}$ pc, we find $\Omega_{\rm{m}} \leq 0.62$, $\omega \leq -0.2$ and $\Omega_{\rm{m}} \leq 0.17$, $\omega \leq -0.65$ (68% c.l.), respectively. As a general result, this analysis shows that if one minimizes $\chi^{2}$ for the parameters $l$, $\Omega_{\rm{m}}$ and $\omega$, the conventional flat $\Lambda$CDM model ($\omega = -1$) with $\Omega_{\rm{m}} = 0.2$ and $l = 22.6 h^{-1}$pc is the best fit for these angular size data.