Speaker
Description
In conventional weak-lensing analyses, the lensing projection is treated
as a direct statistical remapping: the convergence power spectrum inherits from the matter power spectrum, the convergence bispectrum from the matter bispectrum, and so on.
In this work we develop a first-principles theoretical framework that goes beyond this approximate projection scheme. By formulating the dynamics of null geodesic congruences as a path integral, we track how the nonlinear Sachs evolution defines, and distorts, the mapping between the statistical hierarchy of the driving field and that of the observable lensing field.
Within this framework we show, concretely, three effects. First, nonlinear Sachs evolution generates non-Gaussianity in the lensing observables even when the driving fields are exactly Gaussian. Second, non-Gaussianity in the driving fields leaks into the two-point statistics of the lensing observables, a contamination that is invisible to any purely linear projection. Third, we can disentangle, along the line of sight, the contributions from white-noise-type uncorrelated small-scale fluctuations and from correlated stochastic driving components.
Through the mapping to the redshift space, we have also tracked the effects of redshift modifications such as ISW. We emphasise that these effects originate in the nonlinear dynamics of the null geodesic congruence itself, rather than in the mode coupling induced by structure formation. They are therefore not captured by N-body-based studies.