Squeezed Limit non-Gaussianity Estimation with Cosmic Shear

TL;DR

This work introduces a spherical π-field framework to constrain local primordial non-Gaussianity, leveraging the large-scale modulation of small-scale power in weak-lensing maps. By formulating the local power-spectrum field on the sphere and connecting its cross-spectrum with projected fields to the squeezed-limit bispectrum via a non-perturbative model and Gaunt-integral geometry, the method captures squeezed-limit information with a computationally efficient two-point statistic. Validation with the Ulagam N-body simulations demonstrates unbiased $f_{NL}$ recovery in both matter and cosmic-shear fields, while a Fisher forecast for LSST-like data predicts $\sigma_{f_{NL}} \approx 12$ with five tomographic bins and broad soft-$\ell$ coverage. The approach is modular, allowing combination with other $f_{NL}$-sensitive tracers (e.g., kSZ, CMB lensing) to enable joint, variance-reduced estimators, and it explicitly marginalizes gravitational non-Gaussianity through an $A_0$ parameter to control biases. Overall, the π-field cross-spectrum $C_{\kappa\pi}(\ell)$ provides a near-optimal, tractable path to exploiting squeezed-limit PNG information in upcoming surveys like LSST.

Abstract

We present a new method to constrain local primordial non-Gaussianity using the large-scale modulation of the local lensing power spectrum. Our work extends our recently proposed $π$-field method for primordial non-Gaussianity estimation to spherical coordinates and applies it to galaxy lensing. Our approach is computationally efficient and only requires binned multipole power spectra $C_\ell(z_1,z_2)$ on large scales, as well as their covariance. Our method is simpler to implement than a full bispectrum estimator, but still contains the full squeezed-limit information. We validate our model using a suite of N-body simulations and demonstrate its accuracy in recovering the $f_{\mathrm{NL}}$ values. We then perform a Fisher forecast for an LSST-like weak lensing survey, finding $σ_{f_{\mathrm{NL}}} \simeq 12$. Our approach readily combines with other $f_{\mathrm{NL}}$-sensitive fields such as kSZ velocity reconstruction and clustering-based $π$-fields, for a future combined $f_{\mathrm{NL}}$ estimator using various large-scale galaxy and CMB observables.

Figures (14)

• Figure 1: Matter field model.Upper panel: The blue curves show the cross-power spectrum $C_{\delta_m\pi}(\ell)$ for matter fields and $\pi$ fields from Ulagam simulations. The brown lines represent our best-fit models, with the dashed lines showing the contributions from the different terms in our model. The left, middle, and right panels correspond to cosmologies with input $f_{\mathrm{NL}}=0$, $f_{\mathrm{NL}}=100$, and $f_{\mathrm{NL}}=-100$, respectively. The redshift for the matter field is $z = 0.23$, and the high-pass filter $W^{\mathrm{HP}}$ filters out spherical harmonics within $(500, 510)$. Middle panel: The blue curves show the relative error of the simulated cross power spectrum compared with the modeled results. Lower Panel: The MCMC result of $f_{\mathrm{NL}}$ value after marginalizing $A_0$.
• Figure 2: Range of validity of the model for matter.$f_{\mathrm{NL}}$ constraints as a function of $\ell_{\mathrm{max}}$. The black curve shows the result from $f_{\mathrm{NL}} = 0$ simulation subset, the red curve for $f_{\mathrm{NL}} = 100$ subset and blue curve for $f_{\mathrm{NL}} = -100$ subset. Shaded area shows the 1$\sigma$ confidence interval. The matter field shell is at redshift $z = 0.23$ and $\ell\geq5$ (to avoid the simulation tiling regime of Ulagam at this redshift).
• Figure 3: Lensing field model in first of $N_{\mathrm{tomo}} = 3$ case.Upper panel: The blue curves show the cross-power spectrum $C_{\kappa_g\pi}(\ell)$ for lensing convergence fields and $\pi$ fields from Ulagam simulations (using the first bin of three tomographic bins, with $\ell>5$). The brown lines represent our best-fit models, with the dashed lines showing the contributions from the different terms in our model. The left, middle, and right panels correspond to cosmologies with input $f_{\mathrm{NL}}=0$, $f_{\mathrm{NL}}=100$, and $f_{\mathrm{NL}}=-100$, respectively. The error bars are estimated from the scatter across 100 simulations. Here we assume the first of three tomographic bins, and the high-pass filter $W^{\mathrm{HP}}$ filters out spherical harmonics within $(500, 510)$. Middle panel: The blue curves show the relative error of the simulated cross power spectrum compared with the modeled results. Lower Panel: The MCMC result of $f_{\mathrm{NL}}$ value after marginalizing $a_0$.
• Figure 4: Redshift distribution for different tomographic bin numbers under LSST configuration.
• Figure 5: The forecasted constraints on $f_{\mathrm{NL}}$ from cross power spectrum. The curves represent the cumulative information from $\ell_{\mathrm{min}}^{\mathrm{hard}} = 200$ to $\ell_{\mathrm{max}}^{\mathrm{hard}}$. The left panel shows the result with minimum soft mode cut-off $\ell_{\mathrm{min}}^{\mathrm{soft}} = 2$, middle panel with $\ell_{\mathrm{min}}^{\mathrm{soft}} = 10$ and right panel with $\ell_{\mathrm{min}}^{\mathrm{soft}} = 20$. Black curves are result for one tomographic bin. Red curves represent results from three tomographic bins. Blue curves are results for five tomographic bins.