Primordial non-Gaussianity without tails -- how to measure fNL with the bulk of the density PDF

TL;DR

This paper presents a new method to predict and analyze the impact of primordial non-Gaussianity on the late-time cosmic density PDF, enabling precise measurements of the non-Gaussianity parameter fNL from large-scale structure data.

Contribution

The authors develop a novel prediction technique for the density PDF under non-Gaussian initial conditions, achieving high accuracy and demonstrating potential for constraining fNL with upcoming surveys.

Findings

Predictions agree with simulations to 0.2% at z=1 for 30 Mpc/h scale.

Survey analysis can measure fNL with uncertainties of about 7.4 to 46 depending on shape.

Smaller scales and combined analyses improve fNL constraints significantly.

Abstract

We investigate the possibility to detect primordial non-Gaussianity by analysing the bulk of the probability distribution function (PDF) of late-time cosmic density fluctuations. For this purpose we devise a new method to predict the impact of general non-Gaussian initial conditions on the late-time density PDF. At redshift $z=1$ and for a smoothing scale of 30Mpc/$h$ our predictions agree with the high-resolution Quijote N-body simulations to $\sim 0.2\%$ precision. This is within cosmic variance of a $\sim 100(\mathrm{Gpc}/h)^3$ survey volume. When restricting to this 30Mpc/$h$ smoothing scale and to mildly non-linear densities ($\delta[30\mathrm{Mpc}/h] \in [-0.3, 0.4]$) and also marginalizing over potential ignorance of the amplitude of the non-linear power spectrum an analysis of the PDF for such a survey volume can still measure the amplitude of different primordial bispectrum shapes to an accuracy of \smash{$\Delta f_{\mathrm{NL}}^{\mathrm{loc}}=\pm 7.4\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}}=\pm 22.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}}=\pm 46.0$} . When pushing to smaller scales and assuming a joint analysis of the PDF with smoothing radii of 30Mpc/$h$ and 15Mpc/$h$ ($\delta[15\mathrm{Mpc}/h] \in [-0.4, 0.5]$) this improves to \smash{$\Delta f_{\mathrm{NL}}^{\mathrm{loc}}=\pm 3.3\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}}=\pm 11.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}}=\pm 17.0\ $} - even when marginalizing over the non-linear variances at both scales as two free parameters. Especially, such an analysis could simultaneously measure $f_{\mathrm{NL}}$ and the amplitude and slope of the non-linear power spectrum. However, at 15Mpc/$h$ our predictions are only accurate to $\lesssim 0.8\%$ for the considered density range. We discuss how this has to be improved in order to push to these small scales and make full use of upcoming surveys with a PDF-based analysis.