  We propose to use a simple observable, the fractional area of "hot spots" in
weak lensing mass maps which are detected with high significance, to determine
background cosmological parameters. Because these high-shear regions are
directly related to the physical non-linear structures of the universe, they
derive cosmological information mainly from the non-linear regime of density
fluctuations. We show that in combination with future cosmic microwave
background (CMB) anisotropy measurements, this method can place constraints on
cosmological parameters that are comparable to those from the redshift
distribution of galaxy cluster abundances. In particular, adding the
information from this simple shear statistic derived from an LSST-like survey
to CMB anisotropy information from a Planck-like experiment improves the
constraints on the dark energy parameters (energy density and equation of
state) and the normalization of the matter power spectrum by over a factor of
ten. The main advantage of the statistic proposed in this paper is that
projection effects, normally the main source of uncertainty when determining
the presence and the mass of a galaxy cluster, here serve as a source of
information.
