The three-point correlation function of cosmic shear: I. The natural components

摘要: Received ; accepted Abstract. The three-point correlation function of cosmic shear, the weak distortion images distant galaxies by gravitational field inhomogeneous matter distribution in Universe, is studied here. Previous work on statistics shear has mainly concentrated convergence, or aperture measures shear. However, as become clear recently for two-point basic quantity that should be used function: first, it much easier to measure from observational data, since immune against complicated geometries data fields (which contain gaps and holes, e.g. due masking); second, all other (linear) can expressed integrals over function. situation same statistics. contrast function, invariants (with respect rotations) have not been employed yet. Here we consider transformation properties under rotations. We show there are four complex linear combinations components which shall call 'natural components', they multiplied just a phase factor arbitrary rotations, but do mix. In particular, their moduli invariant rotations thus (non-linear) terms these natural components, invariance statistical parity transformations easily obtained. Our results apply only also quantities with mathematical - polar. For example, practically every relation derived here applies polarization microwave background radiation.