Cosmological lensing ratios with DES Y1, SPT and Planck
  Correlations between tracers of the matter density field and gravitational
lensing are sensitive to the evolution of the matter power spectrum and the
expansion rate across cosmic time. Appropriately defined ratios of such
correlation functions, on the other hand, depend only on the angular diameter
distances to the tracer objects and to the gravitational lensing source planes.
Because of their simple cosmological dependence, such ratios can exploit
available signal-to-noise down to small angular scales, even where directly
modeling the correlation functions is difficult. We present a measurement of
lensing ratios using galaxy position and lensing data from the Dark Energy
Survey, and CMB lensing data from the South Pole Telescope and Planck,
obtaining the highest precision lensing ratio measurements to date. Relative to
the concordance $\Lambda$CDM model, we find a best fit lensing ratio amplitude
of $A = 1.1 \pm 0.1$. We use the ratio measurements to generate cosmological
constraints, focusing on the curvature parameter. We demonstrate that
photometrically selected galaxies can be used to measure lensing ratios, and
argue that future lensing ratio measurements with data from a combination of
LSST and Stage-4 CMB experiments can be used to place interesting cosmological
constraints, even after considering the systematic uncertainties associated
with photometric redshift and galaxy shear estimation.
