Physics of non-Gaussian fields and the cosmological genus statistic
  We report a technique to calculate the impact of distinct physical processes
inducing non-Gaussianity on the cosmological density field. A natural
decomposition of the cosmic genus statistic into an orthogonal polynomial
sequence allows complete expression of the scale-dependent evolution of the
morphology of large-scale structure, in which effects including galaxy bias,
nonlinear gravitational evolution and primordial non-Gaussianity may be
delineated. The relationship of this decomposition to previous methods for
analysing the genus statistic is briefly considered and the following
applications are made: i) the expression of certain systematics affecting
topological measurements; ii) the quantification of broad deformations from
Gaussianity that appear in the genus statistic as measured in the Horizon Run
simulation; iii) the study of the evolution of the genus curve for simulations
with primordial non-Gaussianity. These advances improve the treatment of
flux-limited galaxy catalogues for use with this measurement and further the
use of the genus statistic as a tool for exploring non-Gaussianity.
