Equilateral non-Gaussian Bias at the Field Level

TL;DR

This paper addresses the challenge of measuring equilateral primordial non-Gaussianity (PNG) bias in large-scale structure by employing a field-level EFT approach that leverages cosmic variance cancellation. The authors derive a transfer-function-based forward model for halo bias in the presence of equilateral PNG, extract PNG-sensitive parameters from N-body simulations, and demonstrate a nonzero PNG bias coefficient $b_{\psi}$ for massive halos, with a clear redshift and mass dependence. While the results qualitatively align with peak-background-split expectations (increasing $|b_{\psi}|$ with halo mass and redshift), there is a quantitative tension, highlighting limitations of PBS and the importance of a full EFT treatment. They also provide a practical fitting formula for $b_{\psi}(b_1)$ to serve as priors in PNG analyses of current and future galaxy surveys, enabling more robust constraints on equilateral PNG.

Abstract

Primordial non-Gaussianity (PNG) is a common prediction of a wide class of inflationary models. Equilateral-type PNG, generically predicted by single-field inflationary models with higher-derivative interactions, imprints subtle but measurable signatures on the large-scale distribution of matter. An important parameter of these imprints is the PNG-induced bias coefficient $b_ψ$, which quantifies how the abundance and clustering of dark matter halos and galaxies respond to mode coupling in the initial conditions. Measuring $b_ψ$ is important for constraining equilateral PNG, yet it is notoriously challenging due to its degeneracy with Gaussian scale-dependent bias contributions. In this work, we present the first precision measurements of equilateral $b_ψ$ for dark matter halos using effective field theory at the field level. We show that this approach disentangles PNG effects from those of the Gaussian bias by virtue of noise variance cancellation. We compare our results with the phenomenological predictions based on the Peak-Background Split model, finding some agreement at the qualitative level on the redshift and mass dependence, but poor agreement at the quantitative level. We present a fitting formula for $b_ψ$ as a function of the linear bias, which can be used to set priors in PNG searches with ongoing and future galaxy surveys.

Figures (12)

• Figure 1: Scale dependence of the equilateral PNG bias $k^{2}/\mathcal{M}(k)$ at multiple redshifts. The dashed line shows the asymptotic $k^2$ scaling. The shaded region ($0.01<$$k/\,h\,\mathrm{Mpc}^{-1}<$$0.4$ ) indicates the range probed by galaxy surveys.
• Figure 2: Mean and spread of the halo–matter transfer function $\beta_1(k)$ measured from the Gaussian Quijote HR simulations at $z = 0.5$. Each solid curve shows the mean $\beta_1(k)$ across 100 independent realizations for a given halo mass bin, in units of $h^{-1}M_{\odot}$, while the shaded region indicates the full range (minimum to maximum) across the ensemble. For a fixed mass bin, the transfer function is nearly scale-independent on large scales, but exhibits a strong upturn toward smaller scales ($k \gtrsim 0.1 \, h\,\mathrm{Mpc}^{-1}$), with the amplitude increasing systematically with halo mass.
• Figure 3: Halo bias measurements of $b_{\Gamma_3}$ versus $b_{\mathcal{G}_2}$ from 100 Quijote HR simulations with Gaussian initial conditions at $z=0.5$. Each point corresponds to a fit for one simulation and halo mass bin. The black dotted line shows the empirical relation $b_{\Gamma_3} = -2.90b_{\mathcal{G}_2} - 0.13$. The measurements closely follow the linear relation across the full range of $b_{\mathcal{G}_2}$ values.
• Figure 4: Field-level comparison between the simulated halo overdensity field and the best-fit forward model for $z=0.5$ and halo masses $\log M_h$$\in$ [13.0, 13.5] $h^{-1}M_{\odot}$ computed using Hi-Fi mocks. The top row shows the comparison for a simulation with PNG, while the bottom row presents the corresponding comparison for the Gaussian (PNG-free) initial conditions. The left panel shows the simulated halo overdensity slice, $\delta_h^{\mathrm{truth}}$, taken directly from the simulation. The middle panel displays the corresponding best-fit forward-modeled field, $\delta_h^{\mathrm{best-fit}}$, computed by linearly combining the basis operators with the optimal transfer functions. The right panel shows the residual field, $\delta_h^{\mathrm{truth}} - \delta_h^{\mathrm{best-fit}}$, which quantifies the model error.
• Figure 5: Comparison of the field-level bias transfer functions $\beta_1(k), \beta_2(k), \beta_{{\mathcal{G}}_2}(k), \beta_3(k)$, along with the residual power spectrum, $P_{\rm err}(k) \equiv \langle \, | \delta^{\rm best-fit}_h(\mathbf{k}) - \delta^{\rm truth}_h(\mathbf{k}) |^2 \rangle'$, for halo masses $\log M_h$$\in$ [13.5, 14.0] $h^{-1 }M_\odot$ at redshift $z = 0.5$. Results are averaged across the four simulations and shown with (blue) and without (orange) PNG, measured using Hi-Fi mocks. The scale-dependent offset induced by equilateral PNG is visible in the PNG curve.