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

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.

changes to agree with journal version; 22 pages, 12 figures; public code available at https://github.com/OliverFHD/CosMomentum

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