Fisher forecasts for primordial non-Gaussianity from persistent homology

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