Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure

TL;DR

The paper develops and tests a unified Fisher-information framework for constraining local-type primordial non-Gaussianity from two-point LSS statistics by combining sampling-variance cancellation (multi-tracer) with shot-noise suppression (optimal halo weighting). Using large N-body simulations with Gaussian and non-Gaussian initial conditions, it shows that information on $f_{ m NL}$ can be dramatically increased by splitting halos into multiple mass bins and by optimally weighting halos to suppress stochasticity, even when the dark matter field is not observed. When the dark matter field is available, optimal mass weighting and multi-tracer analyses can, in the continuous-limit, achieve near-optimal constraints, with forecasts of $ ilde{\sigma}_{f_{ m NL}} o{ m O}(1)$ for volumes of order $50~h^{-3}{ m Gpc}^3$ and halo masses down to $ oughly 10^{12}~h^{-1}M_\odot$ at $z hicksim 0$, and potentially $ ilde{\sigma}_{f_{ m NL}} o 0.1$ with even deeper/denser surveys. The halo-model predictions align well with the simulations, confirming the central role of the second-order bias and shot-noise structure in extracting $f_{ m NL}$ from two-point statistics. Overall, the work argues that multitracer and shot-noise weighting strategies can substantially improve constraints on primordial non-Gaussianity from current and future LSS data, and can be extended to other PNG models and higher-order statistics.

Abstract

One of the main signatures of primordial non-Gaussianity of the local type is a scale-dependent correction to the bias of large-scale structure tracers such as galaxies or clusters, whose amplitude depends on the bias of the tracers itself. The dominant source of noise in the power spectrum of the tracers is caused by sampling variance on large scales (where the non-Gaussian signal is strongest) and shot noise arising from their discrete nature. Recent work has argued that one can avoid sampling variance by comparing multiple tracers of different bias, and suppress shot noise by optimally weighting halos of different mass. Here we combine these ideas and investigate how well the signatures of non-Gaussian fluctuations in the primordial potential can be extracted from the two-point correlations of halos and dark matter. On the basis of large $N$-body simulations with local non-Gaussian initial conditions and their halo catalogs we perform a Fisher matrix analysis of the two-point statistics. Compared to the standard analysis, optimal weighting- and multiple-tracer techniques applied to halos can yield up to one order of magnitude improvements in $\fnl$-constraints, even if the underlying dark matter density field is not known. We compare our numerical results to the halo model and find satisfactory agreement. Forecasting the optimal $\fnl$-constraints that can be achieved with our methods when applied to existing and future survey data, we find that a survey of $50h^{-1}\mathrm{Gpc}^3$ volume resolving all halos down to $10^{11}\hMsun$ at $z=1$ will be able to obtain $σ_{\fnl}\sim1$ (68% cl), a factor of $\sim20$ improvement over the current limits. Decreasing the minimum mass of resolved halos, increasing the survey volume or obtaining the dark matter maps can further improve these limits, potentially reaching the level of $σ_{\fnl}\sim0.1$. (abridged)

Figures (12)

• Figure 1: Shot noise $\mathcal{E}_{\delta^2}$ of the squared dark matter density field $\delta^2$ as defined in Eq. (\ref{['sigma_dm2']}) with both Gaussian (solid green) and non-Gaussian initial conditions with $f_{\mathrm{NL}}=+100$ (solid red) and $f_{\mathrm{NL}}=-100$ (solid yellow) from $N$-body simulations at $z=0$. Clearly, $\mathcal{E}_{\delta^2}$ is close to white-noise like in all three cases. The auto power spectrum $\langle\left(\delta\!*\!\delta\right)^2\rangle$ of $\delta^2$ in Fourier space (dashed), its cross power spectrum $\langle\left(\delta\!*\!\delta\right)\delta\rangle$ with the ordinary dark matter field $\delta$ (dot-dashed), as well as the ordinary dark matter power spectrum $\langle\delta^2\rangle$ (dotted) are overplotted for the corresponding values of $f_{\mathrm{NL}}$. The squared dark matter field $\delta^2$ can be interpreted as a biased tracer of $\delta$ and therefore shows the characteristic $f_{\mathrm{NL}}$-dependence of biased fields (like halos) on large scales.
• Figure 2: LEFT: Gaussian effective bias (top) and its derivative with respect to $f_{\mathrm{NL}}$ (bottom) for the case of $30$ mass bins. The scale-independent part $\boldsymbol{b}_{\mathrm{G}}$ is plotted in dotted lines for each bin; it was obtained by averaging all modes with $k\le0.032h\mathrm{Mpc}^{-1}$. RIGHT: Large-scale averaged Gaussian effective bias $\boldsymbol{b}_{\mathrm{G}}$ from the left panel (dotted lines) plotted against mean halo mass. The solid line depicts the linear-order bias derived from the peak-background split formalism. All error bars are obtained from the variance of our $12$ boxes to their mean. Results are shown for FOF halos at $z=0$.
• Figure 3: Eigenvalues (left panel) and eigenvectors (right panel) of the shot noise matrix $\boldsymbol{\mathcal{E}}$ for $f_{\mathrm{NL}}=0$ (solid), $+100$ (dashed) and $-100$ (dotted) in the case of $30$ mass bins. Their derivatives with respect to $f_{\mathrm{NL}}$ are plotted underneath. For clarity, only the two eigenvectors $\boldsymbol{V}_{\!\!\pm}$ along with their derivatives are shown in the right panel. The straight dotted line in the upper left panel depicts the value $1/\bar{n}$ and the red (dot-dashed) curve in the top right panel shows $b_2(M)$ computed from the peak-background split formalism, scaled to the value of $\boldsymbol{V}_{\!\!+}$ at $M\simeq3\times10^{13}h^{-1}\mathrm{M}_{\odot}$. Results are shown for FOF halos at $z=0$.
• Figure 4: Relative scale dependence of the effective bias from all FOF (left panel) and SO halos (right panel) resolved in our N-body simulations ($M_{\mathrm{min}}\simeq 5.9\times10^{12}h^{-1}\mathrm{M}_{\odot}$), which are seeded with non-Gaussian initial conditions of the local type with $f_{\mathrm{NL}}=+100,0,-100$ (solid lines and data points from top to bottom). The solid lines show the best fit to the linear theory model of Eq. (\ref{['b(k,fnl)']}), taking into account all the modes to the left of the arrow. The corresponding best-fit values are quoted in the bottom right of each panel. The dotted lines show the model evaluated at the input values $f_{\mathrm{NL}}=+100,0,-100$. The results assume knowledge of the dark matter density field and an effective volume of $V_{\mathrm{eff}}\simeq50h^{-3}\mathrm{Gpc}^3$ at $z=0$.
• Figure 5: Same as Fig. \ref{['fit_u']}, but for weighted halos that have minimum stochasticity relative to the dark matter. Note that the one-sigma errors on $f_{\mathrm{NL}}$ are reduced by a factor of $\sim 5$ compared to uniform weighting. In the case of SO halos the input values for $f_{\mathrm{NL}}$ are well recovered by the best-fit, while FOF halos still show a suppression of $\sim20\%$ ($q\simeq0.8$) in the best-fit $f_{\mathrm{NL}}$.