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Weak gravitational lensing on a cosmological scale can provide strong constraints on both the nature of dark matter and the dark energy equation of state. Most of the current weak lensing studies are restricted to (two‐dimensional) projections, but tomographic studies with photometric redshifts have been started, and future surveys offer the possibility of probing the evolution of structure with redshift. In future we will be able to probe the growth of structure in 3D and put tighter constraints on cosmological models than can be achieved by the use of galaxy redshift surveys alone. Earlier studies in this direction focused mainly on evolution of the 3D power spectrum, but extension to higher‐order statistics can lift degeneracies as well as providing information on primordial non‐Gaussianity. We present analytical results for specific higher‐order descriptors, the bispectrum and trispectrum, as well as collapsed multipoint statistics derived from them, i.e.  cumulant correlators . We also compute quantities we call the  skew‐spectrum  and  kurt‐spectra , which are the Fourier transforms of the well‐known cumulant correlators. We compute the redshift dependence of these objects and study their performance in the presence of realistic noise and photometric redshift errors.

Higher‐order convergence statistics for three‐dimensional weak gravitational lensing