Primordial non-Gaussianity -- Fast simulations and persistent summary statistics

We investigate the sensitivity of topological and traditional summary statistics to primordial non-Gaussianity (PNG) using two suites of simulations. First, we introduce a new simulation suite for PNG, PNG-pmwd, comprising more than $20{,}000$ halo catalogs that vary individually local and equilateral shapes, together with variations in $Ω_m$ and $σ_8$. Second, we carry out a systematic comparison of topological descriptors, as well as powerspectrum and bispectrum measurements, evaluating their constraining power on both local and equilateral $f_{\rm NL}$ and how this sensitivity varies with halo mass. This dataset enables likelihood-free neural regression of $f_{\rm NL}$ across multiple halo mass bins for a wide range of summary statistics. Third, we assess the transferability of these learned mappings by testing whether models trained on fast pmwd simulations can robustly infer on simulations from the QuijotePNG suite. We find that a combination of simple descriptive statistics of the topological features (PD-statistics) leads to the best performance to constrain equilateral PNG. We observe that the constraining power of these summaries comes from large-mass halos, with small-mass halos adding noise and degrading performance. Similarly, we find that the transferability of the learned mappings, for both topological and powerspectrum plus bispectrum, degrades if small scales or small-mass halos are included.

💡 Research Summary

This paper presents a rigorous investigation into the detection and characterization of Primordial Non-Gaussianity (PNG), a crucial probe for understanding the physics of the early universe’s inflationary epoch. The study addresses the challenge of effectively constraining the $f_{\rm NL}$ parameter, specifically focusing on its local and equilateral shapes, through a combination of large-scale simulations and advanced machine learning techniques.

The researchers first developed a novel simulation suite, named PNG-pmwd, which contains over 20,000 halo catalogs. This suite is uniquely designed to vary the $f_{\rm NL}$ shapes (local and equilateral) alongside fundamental cosmological parameters such as $\Omega_m$ and $\sigma_8$. This high-dimensional dataset provides the necessary statistical power to train sophisticated models capable of distinguishing subtle non-Gaussian signals from cosmic variance and other cosmological parameters.

A central component of the research is the comparative analysis between traditional summary statistics—namely the power spectrum and bispectrum—and topological descriptors. By employing likelihood-free neural regression, the authors trained models to infer $f_{\rm NL}$ across various halo mass bins. A significant finding of this study is that the “PD-statistics,” which are simplified descriptive statistics derived from topological features, outperform traditional methods in constraining the equilateral shape of PNG. This suggests that the geometric and topological information encoded in the large-scale structure (LSS) provides a superior signal for certain types of non-Gaussianity that power spectra alone might miss.

Furthermore, the study provides critical insights into the role of halo mass in cosmological inference. The analysis reveals that the constraining power for PNG is primarily driven by large-mass halos, whereas the inclusion of small-mass halos introduces significant noise, thereby degrading the performance of the regression models. This finding has profound implications for future galaxy surveys, suggesting that mass-dependent weighting or filtering is essential for optimal parameter estimation.

Finally, the paper evaluates the transferability of the learned mappings. The authors tested whether models trained on the computationally efficient PNG-pmwd simulations could generalize to the more complex and high-fidelity QuijotePNG suite. The results indicate a degradation in transferability when small-scale or small-mass halo information is included, highlighting a potential domain shift issue. This underscores the necessity of careful calibration and domain adaptation when using fast, approximate simulations to train neural networks intended for application to real-world, high-precision observational data. In summary, this work establishes a powerful new framework for PNG detection using topological statistics and deep learning, while providing essential warnings regarding mass-scale sensitivity and model transferability.