Hierarchical summaries for primordial non-Gaussianities

TL;DR

The paper tackles tightening constraints on local-type primordial non-Gaussianity, $f_{ m NL}$, by proposing a hierarchical estimator that fuses large-scale power spectrum and bispectrum with PatchNet-based field-level compression of small-scale information. Using a Fisher-information approach and Quijote-PNG simulations, the study shows that patch-based summaries provide consistent 30–45% gains at low $k_{ m max}$, capturing information beyond the bispectrum and reducing dependence on highly non-linear modelling. This framework offers a computationally efficient pathway to approach $\sigma_{f_{ m NL}} \sim 1$ for upcoming Stage IV surveys, by leveraging both global statistics and localized neural summaries. The results suggest a scalable, robust method to maximize PNG information while mitigating modelling challenges in the non-linear regime.

Abstract

The advent of Stage IV galaxy redshift surveys such as DESI and Euclid marks the beginning of an era of precision cosmology, with one key objective being the detection of primordial non-Gaussianities (PNG), potential signatures of inflationary physics. In particular, constraining the amplitude of local-type PNG, parameterised by $f_{\rm NL}$, with $σ_{f_{\rm NL}} \sim 1$, would provide a critical test of single versus multi-field inflation scenarios. While current large-scale structure and cosmic microwave background analyses have achieved $σ_{f_{\rm NL}} \sim 5$-$9$, further improvements demand novel data compression strategies. We propose a hybrid estimator that hierarchically combines standard $2$-point and $3$-point statistics with a field-level neural summary, motivated by recent theoretical work that shows that such a combination is nearly optimal, disentangling primordial from late-time non-Gaussianity. We employ PatchNet, a convolutional neural network that extracts small-scale information from sub-volumes (patches) of the halo number density field while large-scale information is retained via the power spectrum and bispectrum. Using Quijote-PNG simulations, we evaluate the Fisher information of this combined estimator across various redshifts, halo mass cuts, and scale cuts. Our results demonstrate that the inclusion of patch-based field-level compression always enhances constraints on $f_{\rm NL}$, reaching gains of $30$-$45\%$ at low $k_{\rm max}$ ($\sim 0.1 \, h \, \text{Mpc}^{-1}$), and capturing information beyond the bispectrum. This approach offers a computationally efficient and scalable pathway to tighten the PNG constraints from forthcoming survey data.

Figures (3)

• Figure 1: Expected uncertainty for the different summary statistics at $z=1$ for two halo-mass cuts as a function of the power spectrum and bispectrum $k_{\text{max}}$. In both cases, the PatchNet information (patches) improves the constraining power of the power spectrum and the power spectrum combined with bispectrum analyses.
• Figure 2: Expected uncertainty for the different summary statistics as a function of the power spectrum and bispectrum $k_{\text{max}}$ at different redshift snapshots. At all redshifts, we applied the same halo-mass cut, $M_{\text{h}} > 3.2 \times M_{\odot} \, h^{-1}$. The patch information adds constraining power at every redshift.
• Figure 3: Expected uncertainty for the different summary statistics at fixed number density over redshifts as a function of the power spectrum and bispectrum $k_{\text{max}}$. At each redshift, we selected a halo-mass cut that has in the fiducial cosmology the same number density of $z=3$ (see Table \ref{['tab:Mmin']}). As in Fig. \ref{['fig:Mcut-zdep']}, the patch information improves the constraining power of the standard summary statistics.