Testing models of vacuum energy interacting with cold dark matter
  We test the models of vacuum energy interacting with cold dark matter and try
to probe the possible deviation from the $\Lambda$CDM model using current
observations. We focus on two specific models, $Q=3\beta H\rho_{\Lambda}$ and
$Q=3\beta H\rho_c$. The data combinations come from the Planck 2013 data, the
baryon acoustic oscillations measurements, the type-Ia supernovae data, the
Hubble constant measurement, the redshift space distortions data and the galaxy
weak lensing data. For the $Q=3\beta H\rho_c$ model, we find that it can be
tightly constrained by all the data combinations, while for the $Q=3\beta
H\rho_{\Lambda}$ model, there still exist significant degeneracies between
parameters. The tightest constraints for the coupling constant are
$\beta=-0.026^{+0.036}_{-0.053}$ (for $Q=3\beta H\rho_{\Lambda}$) and
$\beta=-0.00045\pm0.00069$ (for $Q=3\beta H\rho_c$) at the $1\sigma$ level. For
all the fit results, we find that the null interaction $\beta=0$ is always
consistent with data. Our work completes the discussion on the interacting dark
energy model in the recent Planck 2015 papers. Considering this work together
with the Planck 2015 results, it is believed that there is no evidence for the
models beyond the standard $\Lambda$CDM model from the point of view of
possible interaction.
