Cosmology with Persistent Homology: Parameter Inference via Machine Learning

Building upon [2308.02636], this article investigates the potential constraining power of persistent homology for cosmological parameters and primordial non-Gaussianity amplitudes in a likelihood-free inference pipeline. We evaluate the ability of persistence images (PIs) to infer parameters, compared to the combined Power Spectrum and Bispectrum (PS/BS), and we compare two types of models: neural-based, and tree-based. PIs consistently lead to better predictions compared to the combined PS/BS when the parameters can be constrained (i.e., for $\{\Omega_{\rm m}, \sigma_8, n_{\rm s}, f_{\rm NL}^{\rm loc}\}$). PIs perform particularly well for $f_{\rm NL}^{\rm loc}$, showing the promise of persistent homology in constraining primordial non-Gaussianity. Our results show that combining PIs with PS/BS provides only marginal gains, indicating that the PS/BS contains little extra or complementary information to the PIs. Finally, we provide a visualization of the most important topological features for $f_{\rm NL}^{\rm loc}$ and for $\Omega_{\rm m}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for $\Omega_{\rm m}$, while $f_{\rm NL}^{\rm loc}$ uses the filaments (1-cycles) in addition to the other two types of topological features.