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

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 $p_x=\omega {\rho }_x$ ($-1 \leq \omega < 0$)\mathrm{.}Theallowedintervalsfor$\omega$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,wefind$\Omega_{\rm{m}} \leq 0.62$,$\omega \leq -0.2$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 $l$, ${\mathrm{\Omega }}_{\mathrm{m}}$ and $\omega$, the conventional flat $\mathrm{\Lambda }$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.