The late-time matter density PDF at a given smoothing scale is mostly sensitive to the skewness of the primordial density field at that scale and to the running of that skewness around the smoothing scale. As such – unless the PDF is measured on a wide range of smoothing scales – it can only poorly distinguish between different primordial bispectrum shapes. Any model that produces mainly one of the possible bispectrum template can however be successfully tested with PDF measurements. In this paper, we consider an analysis of the PDF at redshift z = 1 in a survey volume of V = 100(Gpc h−1)3, which is smaller than the effective volume of upcoming surveys such as Spherex with Veff ≈ 150(Gpc h−1)3 and somewhat larger than existing surveys such as BOSS with Veff ≈ 55(Gpc h−1)3 (Doré et al. 2014; Alam et al. 2017). At a smoothing scale of 30 Mpc h−1 we find our PDF model to agree with the high-resolution run of the Quijote N-body simulations (Villaescusa-Navarro et al. 2019) to $\lesssim 0.2{{\ \rm per\ cent}}$ accuracy over a range of δ[30 Mpc h−1] ∈ [−0.3, 0.4]. This is within cosmic variance of the considered volume of 100(Gpc h−1)3 (which is also the combined volume of the Quijote high-resolution boxes). Restricting to this smoothing scale and to these mildly non-linear densities we find that a PDF based analysis can measure the amplitude of different primordial bispectrum shapes to an accuracy of $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 7.4\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 22.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 46.0$ – even when marginalizing over the non-linear variance of the density field as a free parameter. 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 can simultaneously measure fNL and the amplitude and slope of the non-linear power spectrum. Note that any dependence of these forecasts on σ8 is completely mitigated by this marginalization. We do not consider the impact of Ωm on our signals (see Uhlemann et al. 2019, for an investigation of the general cosmology dependence of the PDF) though Friedrich et al. (2018) and Gruen et al. (2018) have demonstrated that parameters of the ΛCDM model and higher order moments of the density field can be measured simultaneously from what they call lensing-around-cells. Ultimately, we are working towards a combination of a late-time PDF analysis with the early-universe results of Planck Collaboration IX (2019). These two analyses have the potential to complement each other: the CMB providing information about the background ΛCDM space–time, the late-time density PDF providing information about non-linear structure growth and both of them containing independent information about the imprint of primordial non-Gaussianities on the large-scale structure.
Citation: Alam et al. 2017
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