Cosmology with Persistent Homology: Parameter Inference via Machine Learning
🤖 AI Summary
This study investigates the potential of persistent homology (PH) for constraining cosmological parameters and primordial non-Gaussianity—particularly the local bispectrum amplitude (f_{
m NL}^{
m loc}). We propose a likelihood-free machine learning framework based on persistence images (PIs), integrating neural networks and XGBoost for parameter inference, and systematically compare its performance against the conventional power spectrum and bispectrum (PS/BS) combination. We demonstrate, for the first time, that PIs significantly outperform PS/BS in inference precision for key parameters—especially (f_{
m NL}^{
m loc})—while their joint use yields negligible improvement. Topological dimension decomposition reveals that 0D features dominate (Omega_m) constraints, 1D (filamentary) structures exhibit specific sensitivity to (f_{
m NL}^{
m loc}), and 2D voids also contribute to (Omega_m) modeling. These results establish PH as a physically interpretable, novel topological probe for analyzing the cosmic large-scale structure.
Application Category
📝 Abstract
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 ${Omega_{
m m}, sigma_8, n_{
m s}, f_{
m NL}^{
m loc}}$). PIs perform particularly well for $f_{
m NL}^{
m loc}$, 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 $f_{
m NL}^{
m loc}$ and for $Omega_{
m m}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for $Omega_{
m m}$, while $f_{
m NL}^{
m loc}$ uses the filaments (1-cycles) in addition to the other two types of topological features.
Problem
Research questions and friction points this paper is trying to address.
Investigating persistent homology for cosmological parameter inference
Comparing persistence images to power spectrum and bispectrum methods
Identifying key topological features for primordial non-Gaussianity constraints
Innovation
Methods, ideas, or system contributions that make the work stand out.
Persistence Images for cosmological parameter inference
Machine learning pipeline for likelihood-free inference
Topological features analysis via persistent homology
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