Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

Abstract

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 $\Delta f_{\mathrm{NL}}^{\mathrm{loc}}\sim 16$ and $\Delta f_{\mathrm{NL}}^{\mathrm{equi}}\sim 41$ 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.

arXiv comment29 pages, 12 figures, matches published version on JCAP

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• Quijote-PNG: Simulations of primordial non-Gaussianity and the information content of the matter field power spectrum and bispectrum
• Persistent homology in cosmic shear II: A tomographic analysis of DES-Y1
• Quijote-PNG: Quasi-maximum likelihood estimation of Primordial Non-Gaussianity in the non-linear dark matter density field
• Fitting covariance matrix models to simulations
• Wasserstein distance as a new tool for discriminating cosmologies through the topology of large scale structure
• Quijote PNG: The information content of the halo power spectrum and bispectrum