Cosmology with Persistent Homology: Parameter Inference via Machine Learning

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 Omegarm m, σ8, nrm s, frm NLrm loc. PIs perform particularly well for frm NLrm 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 frm NLrm loc and for Omegarm m. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for Omegarm m, while frm NLrm loc is additionally informed by filaments (1-cycles).