  The late-time effect of primordial non-Gaussianity offers a window into the
physics of inflation and the very early Universe. In this work we study the
consequences of a particular class of primordial non-Gaussianity that is fully
characterized by initial density fluctuations drawn from a non-Gaussian
probability density function, rather than by construction of a particular form
for the primordial bispectrum. We numerically generate multiple realisations of
cosmological structure and use the late-time matter power spectrum, bispectrum
and trispectrum to determine the effect of these modified initial conditions.
We show that the initial non-Gaussianity has only a small imprint on the first
three polyspectra, when compared to a standard Gaussian cosmology. Furthermore,
some of our models present an interesting scale-dependent deviation from the
Gaussian case in the bispectrum and trispectrum, although the signal is at most
at the percent level. The majority of our models are consistent with CMB
constraints on the trispectrum, while the others are only marginally excluded.
Finally, we discuss further possible extensions of our study.
