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 $p_x = ωρ_x$ ($-1 \leq ω< 0$). The allowed intervals for $ω$ and $Ω_{\rm{m}}$ are heavily dependent on the value of the mean projected linear size $l$. For $l \simeq 20h^{-1} - 30h^{-1}$ pc, we find $Ω_{\rm{m}} \leq 0.62$, $ω\leq -0.2$ and $Ω_{\rm{m}} \leq 0.17$, $ω\leq -0.65$ (68% c.l.), respectively. As a general result, this analysis shows that if one minimizes $χ^{2}$ for the parameters $l$, $Ω_{\rm{m}}$ and $ω$, the conventional flat $Λ$CDM model ($ω= -1$) with $Ω_{\rm{m}} = 0.2$ and $l = 22.6 h^{-1}$pc is the best fit for these angular size data.