Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology
  We study the information content of summary statistics built from the
multi-scale topology of large-scale structures on primordial non-Gaussianity of
the local and equilateral type. We use halo catalogs generated from numerical
N-body simulations of the Universe on large scales as a proxy for observed
galaxies. Besides calculating the Fisher matrix for halos in real space, we
also check more realistic scenarios in redshift space. Without needing to take
a distant observer approximation, we place the observer on a corner of the box.
We also add redshift errors mimicking spectroscopic and photometric samples. We
perform several tests to assess the reliability of our Fisher matrix, including
the Gaussianity of our summary statistics and convergence. We find that the
marginalized 1-$\sigma$ uncertainties in redshift space are $\Delta f_{\rm
NL}^{\rm loc} \sim 16$ and $\Delta f_{\rm NL}^{\rm equi} \sim 41 $ on a survey
volume of $1$ $($Gpc$/h)^3$. These constraints are weakly affected by redshift
errors. We close by speculating as to how this approach can be made robust
against small-scale uncertainties by exploiting (non)locality.
