Measurement of a Cosmographic Distance Ratio with Galaxy and CMB Lensing

We measure the gravitational lensing shear signal around dark matter halos hosting CMASS galaxies using light sources at $z\sim 1$ (background galaxies) and at the surface of last scattering at $z\sim 1100$ (the cosmic microwave background). The galaxy shear measurement uses data from the CFHTLenS survey, and the microwave background shear measurement uses data from the {\it Planck} satellite. The ratio of shears from these cross-correlations provides a purely geometric distance measurement across the longest possible cosmological lever arm. This is because the matter distribution around the halos, including uncertainties in galaxy bias and systematic errors such as miscentering, cancels in the ratio for halos in thin redshift slices. We measure this distance ratio in three different redshift slices of the CMASS sample, and combine them to obtain a $17\%$ measurement of the distance ratio, $r=0.390^{+0.070}_{-0.062}$ at an effective redshift of $z=0.53$. This is consistent with the predicted ratio from the {\it Planck} best-fit $\Lambda$CDM cosmology of $r=0.419$.