Cosmology with Persistent Homology: Parameter Inference via Machine Learning

Abstract

Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability of Persistence Images (PIs) to infer parameters, comparing them to the combined Power Spectrum and Bispectrum (PS/BS). We also compare two classes of models: neural-based and tree-based. PIs consistently lead to better predictions compared to the combined PS/BS for parameters that can be constrained, i.e., for $\{{\Omega }_{\mathrm{m}},{\sigma }_8,n_{\mathrm{s}},f_{\mathrm{NL}}^{\mathrm{loc}}\}$. PIs perform particularly well for $f_{\mathrm{NL}}^{\mathrm{loc}}$, highlighting the potential of persistent homology for constraining primordial non-Gaussianity. Our results indicate that combining PIs with PS/BS provides only marginal gains, indicating that the PS/BS contains little additional or complementary information to the PIs. Finally, we provide a visualization of the most important topological features for $f_{\mathrm{NL}}^{\mathrm{loc}}$ and for ${\Omega }_{\mathrm{m}}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for ${\Omega }_{\mathrm{m}}$, while $f_{\mathrm{NL}}^{\mathrm{loc}}$ is additionally informed by filaments (1-cycles).

28 pages, 9 figures, 4 tables. Accepted for publication in JCAP. Replaced with the accepted version (minor changes)

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