The effect of primordial non-Gaussianity on the skeleton of cosmic shear
  maps
  (abridged) We explore the imprints of deviations from Gaussian primordial
density fluctuations on the skeleton of the large-scale matter distribution as
mapped through cosmological weak lensing. We computed the skeleton length of
simulated effective convergence maps covering $\sim 35$ sq. deg each, extracted
from a suite of cosmological $n-$body runs with different levels of local
primordial non-Gaussianity. The latter is expected to alter the structure
formation process with respect to the fiducial Gaussian scenario, and thus to
leave a signature on the cosmic web. We found that alterations of the initial
conditions consistently modify both the cumulative and the differential
skeleton length, although the effect is generically smaller than the cosmic
variance and depends on the smoothing of the map prior to the skeleton
computation. Nevertheless, the qualitative shape of these deviations is rather
similar to their primordial counterparts, implying that skeleton statistics
retain good memory of the initial conditions. We performed a statistical
analysis in order to find out at what Confidence Level primordial
non-Gaussianity could be constrained by the skeleton test on cosmic shear maps
of the size we adopted. At 68.3% Confidence Level we found an error on the
measured level of primordial non-Gaussianity of $\Delta f_\mathrm{NL}\sim 300$,
while at 90% Confidence Level it is of $\Delta f_\mathrm{NL}\sim 500$. While
these values by themselves are not competitive with the current constraints,
weak lensing maps larger than those used here would have a smaller
field-to-field variance, and thus would likely lead to tighter constraints. A
rough estimate indicates $\Delta f_\mathrm{NL} \sim$ a few tens at 68.3%
Confidence Level for an all-sky weak lensing survey.
