A Limit on the Cosmological Mass Density and Power Spectrum from the Rotation Curves of Low Surface Brightness Galaxies

We present a method for defining higher order moments of a spin-2 field on the sky using the transformation properties of these statistics under rotation and parity. For the three-point function of the cosmic shear, we show that the eight logically possible combinations of the shear in three points can be divided into two classes; four combinations are even under parity transformations, and four are odd. We compute the expected value of the even-parity ones in the nonlinear regime using the halo model and conclude that on small scales, of the four combinations there is one that is expected to carry most of the signal for triangles close to isosceles. On the other hand, for collapsed triangles, all four combinations are expected to have roughly the same level of signal, although some of the combinations are negative and others positive. We estimate that a survey of a few square degrees area is enough to detect this signal above the noise at arcminute scales.