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

Abstract

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 30 Mpc h−1 our predictions agree with the high-resolution Quijote N-body simulations to $\sim 0.2{{\ \rm per\ cent}}$ precision. This is within cosmic variance of a ∼100(Gpc h−1)3 survey volume. When restricting to this 30 Mpc h−1 smoothing scale and to mildly non-linear densities (δ[30 Mpc h−1] ∈ [−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 $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 7.4\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 22.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 46.0$. When pushing to smaller scales and assuming a joint analysis of the PDF with smoothing radii of 30 and 15 Mpc h−1 (δ[15 Mpc h−1] ∈ [−0.4, 0.5]) this improves to $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 3.3\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 11.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 17.0$ – even when marginalizing over the non-linear variances at both scales as two free parameters. Especially, such an analysis could simultaneously measure fNL and the amplitude and slope of the non-linear power spectrum. However, at 15 Mpc h−1 our predictions are only accurate to $\lesssim 0.8{{\ \rm per\ cent}}$ 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.