Field-Level Inference of Primordial Non-Gaussianity with the Quijote Simulation Suite

Abstract

Local primordial non-Gaussianity, parameterised as $f_{\rm NL}^{\rm local}$, will be stringently constrained using state-of-the-art methods applied to next-generation galaxy redshift survey data. In this paper, in preparation for the upcoming data sets, we demonstrate for the first time the joint field-level inference of $f_{\rm NL}^{\rm local}$, nuisance parameters, and the initial conditions in realistic halo catalogues, ones which are generated through full dark-matter-only $N$-body simulations. The field-level inference algorithm optimally constrains $f_{\rm NL}^{\rm local}$ through a Bayesian forward-modelling approach at the field level, which outperforms traditional methods by leveraging the full statistical power of the data at the scales considered. In addition, we assess its performance under various design choices in the forward model, including tests of the structure formation model and resolution. We demonstrate the robustness of our approach by applying it to a subset of the \textit{Quijote} simulation suite, performing the inference at scales down to $k_{\rm max} \approx 0.1 h \rm{Mpc}^{-1}$. Compared with a power spectrum and bispectrum estimator, we find a $\sim1.3$ improvement in $σ(f_{\rm NL}^{\rm local})$ when applying \borg{}, while marginalising over the initial conditions and bias parameters. From the small-scale information sensitivity tests, we show that the constraints on $f_{\rm NL}^{\rm local}$ improve as we increase the resolution of the inference. These findings underscore the transformative potential of field-level inference to leverage the information available in ongoing surveys such as \textit{Euclid}, providing accurate insights into the physics of cosmic inflation and the number of fields driving it.

Figures (18)

• Figure 1: Comparison of constraints on $f_{\mathrm{NL}}^{\mathrm{local}}$ from two different techniques in the Quijote simulation suite. The grey posteriors represent the Fisher constraints using a combination of power spectrum and bispectrum estimators. The blue posterior shows the constraints on $f_{\mathrm{NL}}$ from a BORG analysis, with an uncertainty of $\sigma(f_\mathrm{NL}) = 23$. The mean and the uncertainty of the posterior is estimated from the weighted mean and the total standard deviation of the runs performed. The vertical dashed line indicates the fiducial value $f_{\mathrm{NL}} = 0$. The results showcase the possible constraints on ${f_\mathrm{NL}}$ at the given resolution of $k_{\rm max} \approx 0.1 h\;\text{Mpc}^{-1}$ when using a field-level inference method to the Quijote-PNG suite over a traditional estimator. The description of the computation of the forecasted constraints is provided in Section \ref{['sec:fisher_method']}.
• Figure 2: Illustration of the forward model used in this study. The model transforms a given set of initial conditions into a predicted halo field, incorporating key features such as the perturbation of the primordial gravitational potential by ${f_\mathrm{NL}}$ and scale-dependent terms in the galaxy bias model. The predicted halo field is then compared to the observed data through voxel-level likelihood evaluation. For more details, see Section \ref{['Method']}.
• Figure 3: Marginalised posteriors of the bias parameters and ${f_\mathrm{NL}}$ for three simulations with fixed initial conditions and ${f_\mathrm{NL}^{\rm gt}}$ values. The results demonstrate that the forward model, including the galaxy bias model, successfully recovers the fiducial ${f_\mathrm{NL}^{\rm gt}}$. These results also provide an estimate for $\sigma_{\rm G}$, which is used in subsequent runs, with the initial conditions fixed to their ground truth values.
• Figure 4: The top three panels show the cross-correlation between the inferred and ground-truth halo fields, while the bottom three panels present the cross-correlation between the inferred and ground-truth dark matter density fields. Each cross-spectra is for the same set of fixed initial condition inferences. The decorrelation in the dark matter density cross-correlation arises from model discrepancies in the structure formation model compared to the $N$-body simulations. In the halo field cross-correlation, the model mismatch at smaller scales likely stems from limitations in both the galaxy bias and structure formation models. These results correspond to fixed initial conditions, and analyses and data at $z=0.5$; for results based on sampled initial conditions, see Figure \ref{['fig:mr_cross_pk']}.
• Figure 5: Comparison of inferred $f_{\rm NL}$ values over 30 simulations, split up between positive ${f_\mathrm{NL}^{\rm gt}}$ (top row), null ${f_\mathrm{NL}^{\rm gt}}$ (middle row), and negative ${f_\mathrm{NL}^{\rm gt}}$ (bottom row). The error bars represent the uncertainty $\sigma(f_\mathrm{NL})$, and the horizontal dashed lines represent the ground-truth ${f_\mathrm{NL}^{\rm gt}}$ value. The results showcase the capability of the field-level inference algorithm to recover the ${f_\mathrm{NL}^{\rm gt}}$ while also marginalising over initial conditions and bias parameters (with $b_{\phi}$ and $b_{\phi\delta}$ fixed as in Eqs. \ref{['eq:bp']} and \ref{['eq:bpd']}).