Cosmology with Persistent Homology: Parameter Inference via Machine Learning

TL;DR

This paper demonstrates that persistent homology, through Persistence Images, effectively constrains cosmological parameters and primordial non-Gaussianity, outperforming traditional spectral methods in a likelihood-free machine learning framework.

Contribution

It introduces the use of Persistence Images in a machine learning pipeline for cosmological parameter inference, showing superior performance over Power Spectrum and Bispectrum methods.

Findings

Persistence Images outperform PS/BS in parameter prediction.

PIs are particularly effective for constraining $f_{NL}^{loc}$.

Combining PIs with PS/BS yields marginal improvements.

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 $\{\Omega_{\rm m}, \sigma_8, n_{\rm s}, f_{\rm NL}^{\rm loc}\}$. PIs perform particularly well for $f_{\rm NL}^{\rm loc}$, 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 $f_{\rm NL}^{\rm loc}$ and for $\Omega_{\rm m}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for $\Omega_{\rm m}$, while $f_{\rm NL}^{\rm loc}$ is additionally informed by filaments (1-cycles).