The Atacama Cosmology Telescope: Constraints on Local Non-Gaussianity from the ACT Cluster Catalog

TL;DR

This work uses the ACT DR6 SZ cluster catalog to constrain local-type primordial non-Gaussianity via the high-mass end of the halo mass function. A forward-model framework employing a Log–Edgeworth halo mass function connects $f_{ m NL}$ to observable cluster counts, incorporating completeness, a mass-observable response, and a weak-lensing-calibrated mass bias. The analysis finds $f_{ m NL}=55.3\pm125$ (68% CL), consistent with Gaussian initial conditions, while a residual mass bias of about $16.4\%$ is favored by the data and helps match observed counts without significantly altering the PNG constraint. The results probe comoving scales of $5$–$10\,\mathrm{Mpc}\,h^{-1}$, complementing CMB bispectrum and scale-dependent bias measurements, and underscore the pivotal role of accurate mass calibration; upcoming SZ and lensing surveys are expected to tighten cluster-based PNG tests further.

Abstract

We derive constraints on local-type primordial non-Gaussianity using the ACT DR6 Sunyaev--Zel'dovich cluster catalog. Modeling the redshift- and mass-dependent number counts of 1,201 clusters in the 10,347~deg$^2$ Legacy region, and accounting for survey completeness, intrinsic SZ scatter, and a weak-lensing-calibrated mass bias, we compute theoretical abundances using the Log--Edgeworth halo mass function. Assuming $Λ$CDM with well-motivated external priors, we obtain $f_{\rm NL} = 55 \pm 125$ (68% CL), consistent with Gaussian initial conditions. These constraints probe comoving scales of $5$--$10~{\rm Mpc}~h^{-1}$, complementing CMB bispectrum and scale-dependent bias measurements, which do not reach such small scales. We also find evidence for a 16.4% residual mass bias, which, although heavily informed by our adopted priors, plays a key role in matching observed and predicted counts but has negligible effect on $f_{\rm NL}$ constraints. We briefly discuss robustness of the results under relaxed priors and the prospects for next-generation SZ and lensing surveys to strengthen cluster-based tests of primordial non-Gaussianity.

Figures (5)

• Figure 1: Joint $f_{\rm NL}$–$\sigma_8$ (left) and $\ln(1-b)$–$f_{\rm NL}$ (right) posteriors for the three cases mentioned in Table \ref{['tab:priors']}. Prior information for $\sigma_8$ and $\ln(1-b)$ is shown as $1\sigma$ grey bands in the 1D marginals as discussed in the text. The $f_{\rm NL}$ posterior is robust to prior choices. The 3 points highlighted in the figure are used in later analysis and are as follows: P1 corresponds to the baseline best fit with $f_{\rm NL} = 55.3$, $\sigma_8 =0.809$ (blue curve in Fig. \ref{['fig:model-comparison-a']}), P2 corresponds to $f_{\rm NL} = 430$, $\sigma_8 =0.78$ (orange curve in Fig. \ref{['fig:model-comparison-a']}). P3 corresponds to $f_{\rm NL} = 430$, $\sigma_8 =0.809$ (green curve in Fig. \ref{['fig:model-comparison-a']}). The other parameters remain fixed at the best fit values for the baseline case.
• Figure 2: Joint $f_{\rm NL}$–$\Omega_m$ (left) and $\ln(1-b)$–$\Omega_m$ (right) posteriors for the three cases mentioned in Table \ref{['tab:priors']}. Prior information for $\Omega_m$ and $\ln(1-b)$ is shown as $1\sigma$ grey bands in the 1D marginals, as discussed in the text. While the $\Omega_m$ and mass bias posteriors overcome the priors, the $f_{\rm NL}$ posterior is robust to prior choices.
• Figure 3: Figure (a) shows a model comparison of cluster counts across redshift bins. Each panel shows the binned number of objects (Counts) as a function of $\log_{10} M_{500c}\,[M_\odot]$ for a different redshift interval: $z\in[0.4,0.5)$ (left), $z\in[0.7,0.8)$ (middle), and $z\in[1.0,1.1)$ (right). Open white circles with error bars represent the measured counts (shown as Data $\pm\sqrt{N}$). Colored curves show model predictions for different parameter choices. The comparison highlights the degeneracy between $\sigma_8$ and $f_{\mathrm{NL}}$, where distinct parameter combinations produce nearly identical number counts across all redshift bins. Note also that the $f_{\rm NL} =0$ plot would be very close to the blue/orange curves. Figure (b) shows the prior and posterior bands on the expected cluster number counts. This shows that the data is informative and constrains the number counts into a thin strip in the counts-mass plane for each redshift bin.
• Figure 4: $R(M,z)=0$ in the $(\log_{10}M,z)$ plane for several negative $f_{\rm NL}$.
• Figure 5: Posterior of $f_{\rm NL}$ (solid: median; dashed: 68% CI).