ZKDR Distance, Angular Size and Phantom Cosmology
  The influence of mass inhomogeneities on the angular size-redshift test is investigated for a large class of flat cosmological models driven by dark energy plus a cold dark matter component. The results are presented in two steps. First, the mass inhomogeneities are modeled by a generalized Zeldovich-Kantowski-Dyer-Roeder (ZKDR) distance which is characterized by a smoothness parameter $\alpha(z)$ and a power index $\gamma$, and, second, we provide a statistical analysis to angular size data for a large sample of milliarcsecond compact radio sources. By marginalizing over the characteristic angular size $l$, fixing $\Omega_M = 0.26$ and assuming a Gaussian prior on $\omega$, i.e., $\omega = -1 \pm 0.3$, the best fit values are $\omega = -1.03$ and $\alpha = 0.9$. By assuming a Gaussian prior on the matter density parameter, i.e., $\Omega_M = 0.3 \pm 0.1$, the best fit model for a phantom cosmology with $\omega = -1.2$ occurs at $\Omega_M = 0.29$ and $\alpha = 0.9$ when we marginalize over the characteristic size of the compact radio sources. The results discussed here suggest that the ZKDR distance can give important corrections to the so-called background tests of dark energy. 
R. C. Santos, J. A. S. Lima