Combining Size and Shape in Weak Lensing
  Weak lensing alters the size of images with a similar magnitude to the
distortion due to shear. Galaxy size probes the convergence field, and shape
the shear field, both of which contain cosmological information. We show the
gains expected in the Dark Energy Figure of Merit if galaxy size information is
used in combination with galaxy shape. In any normal analysis of cosmic shear,
galaxy sizes are also studied, so this is extra statistical information comes
for free and is currently unused. There are two main results in this letter:
firstly, we show that size measurement can be made uncorrelated with
ellipticity measurement, thus allowing the full statistical gain from the
combination, provided that $\sqrt{Area}$ is used as a size indicator; secondly,
as a proof of concept, we show that when the relevant modes are
noise-dominated, as is the norm for lensing surveys, the gains are substantial,
with improvements of about 68% in the Figure of Merit expected when systematic
errors are ignored. An approximate treatment of such systematics such as
intrinsic alignments and size-magnitude correlations respectively suggests that
a much better improvement in the Dark Energy Figure of Merit of even a factor
of ~4 may be achieved.
