3D weak lensing

I propose an analysis method, based on spin-spherical harmonics and spherical Bessel functions, for large-scale weak lensing surveys which have source-distance information through photometric redshifts. I show that the distance information can significantly reduce statistical errors on cosmological parameters; in particular, 3D lensing analysis offers excellent prospects for constraining the equation of state of the vacuum energy which dominates the energy density of the Universe. I show that the ratio of pressure to energy density could be determined to an accuracy of similar to1 per cent or better. Having distance information also offers significant advantages in the control of systematic effects such as the intrinsic alignment of galaxies. The case for obtaining photometric redshifts is therefore compelling. A signal-to-noise eigenmode analysis of the modes shows that the modes with highest signal-to-noise ratio correspond quite closely to ignoring the redshift information, but there is significant extra information from a few radial modes. These modes are generally long-wavelength, suggesting that useful information can be gleaned even if the photometric redshifts are relatively inaccurate.