3D Photometric Cosmic Shear
  Here we present a number of improvements to weak lensing 3D power spectrum
analysis, 3D cosmic shear, that uses the shape and redshift information of
every galaxy to constrain cosmological parameters. We show how photometric
redshift probability distributions for individual galaxies can be directly
included in this statistic with no averaging. We also include the Limber
approximation, considerably simplifying full 3D cosmic shear analysis, and we
investigate its range of applicability. Finally we show the relationship
between weak lensing tomography and the 3D cosmic shear field itself; the steps
connecting them being the Limber approximation, a harmonic-space transform and
a discretisation in wavenumber. Each method has its advantages: 3D cosmic shear
analysis allows straightforward inclusion of all relevant modes, thus ensuring
minimum error bars, and direct control of the range of physical wavenumbers
probed, to avoid the uncertain highly nonlinear regime. On the other hand,
tomography is more convenient for checking systematics through direct
investigation of the redshift dependence of the signal. Finally, for
tomography, we suggest that the angular modes probed should be
redshift-dependent, to recover some of the 3D advantages.
