Constraints and tensions in testing general relativity from Planck and
  CFHTLenS including intrinsic alignment systematics
  We present constraints on testing general relativity (GR) at cosmological
scales using recent data sets and assess the impact of galaxy intrinsic
alignment (IA) in the CFHTLenS lensing data on those constraints. We consider
CMB temperature data from Planck, the galaxy power spectrum from WiggleZ, weak
lensing tomography from the CFHTLenS, ISW-galaxy cross correlations, and BAO
data from 6dF, SDSS DR7, and BOSS DR9. We use a parameterization of the
modified gravity (MG) that is binned in redshift and scale, a parameterization
that evolves monotonically in scale but is binned in redshift, and a functional
parameterization that evolves only in redshift. We present the results in terms
of the MG parameters $Q$ and $\Sigma$. We employ an IA model with an amplitude
$A_{CFHTLenS}$ that is included in the parameter analysis. We find an
improvement in the constraints on the MG parameters corresponding to $40-53\%$
increase on the figure of merit compared to previous studies, and GR is found
consistent with the data at the $95\%$ CL. The bounds found on $A_{CFHTLenS}$
are sensitive to the MG parameterization used, and the correlations between
$A_{CFHTLenS}$ and MG parameters are found to be weak to moderate. For all 3 MG
parameterizations $A_{\rm CFHTLenS}$ is found consistent with zero when the
whole lensing sample is used, however, when using the optimized early-type
galaxy sample a significantly non-zero $A_{\rm CFHTLenS}$ is found for GR and
the third MG parameterization. We find that the tensions observed in previous
studies persist, and there is an indication that CMB data and lensing data
prefer different values for MG parameters, particularly for the parameter
$\Sigma$. The analysis of the confidence contours and probability distributions
suggest that the bimodality found follows that of the known tension in the
$\sigma_8$ parameter. (Abridged)
