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We study the connection of matter density and its tracers from the probability density function (PDF) perspective. One aspect of this connection is the conditional expectation value 〈δtracer|δm〉 when averaging both tracer and matter density over some scale. We present a new way to incorporate a Lagrangian bias expansion of this expectation value into standard frameworks for modelling the PDF of density fluctuations and counts-in-cells statistics. Using N-body simulations and mock galaxy catalogues we confirm the accuracy of this expansion and compare it to the more commonly used Eulerian parametrization. For haloes hosting typical luminous red galaxies, the Lagrangian model provides a significantly better description of 〈δtracer|δm〉 at second order in perturbations. A second aspect of the matter-tracer connection is shot-noise, i.e. the scatter of tracer density around 〈δtracer|δm〉. It is well known that this noise can be significantly non-Poissonian and we validate the performance of a more general, two-parameter shot-noise model for different tracers and simulations. Both parts of our analysis are meant to pave the way for forthcoming applications to survey data. [ABSTRACT FROM AUTHOR]

Measurements of large-scale structure are interpreted using theoretical predictions for the matter distribution, including potential impacts of baryonic physics. We constrain the feedback strength of baryons jointly with cosmology using weak lensing and galaxy clustering observables (3 × 2pt) of Dark Energy Survey (DES) Year 1 data in combination with external information from baryon acoustic oscillations (BAO) and Planck cosmic microwave background polarization. Our baryon modelling is informed by a set of hydrodynamical simulations that span a variety of baryon scenarios; we span this space via a Principal Component (PC) analysis of the summary statistics extracted from these simulations. We show that at the level of DES Y1 constraining power, one PC is sufficient to describe the variation of baryonic effects in the observables, and the first PC amplitude (Q 1) generally reflects the strength of baryon feedback. With the upper limit of Q 1 prior being bound by the Illustris feedback scenarios, we reach |$\sim 20{{\ \rm per\ cent}}$| improvement in the constraint of |$S_8=\sigma _8(\Omega _{\rm m}/0.3)^{0.5}=0.788^{+0.018}_{-0.021}$| compared to the original DES 3 × 2pt analysis. This gain is driven by the inclusion of small-scale cosmic shear information down to 2.5 arcmin, which was excluded in previous DES analyses that did not model baryonic physics. We obtain |$S_8=0.781^{+0.014}_{-0.015}$| for the combined DES Y1+Planck EE+BAO analysis with a non-informative Q 1 prior. In terms of the baryon constraints, we measure |$Q_1=1.14^{+2.20}_{-2.80}$| for DES Y1 only and |$Q_1=1.42^{+1.63}_{-1.48}$| for DESY1+Planck EE+BAO, allowing us to exclude one of the most extreme AGN feedback hydrodynamical scenario at more than 2σ. [ABSTRACT FROM AUTHOR]

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 f NL 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. [ABSTRACT FROM AUTHOR]

Computing the inverse covariance matrix (or precision matrix) of large data vectors is crucial in weak lensing (and multiprobe) analyses of the large-scale structure of the Universe. Analytically computed covariances are noise-free and hence straightforward to invert; however, the model approximations might be insufficient for the statistical precision of future cosmological data. Estimating covariances from numerical simulations improves on these approximations, but the sample covariance estimator is inherently noisy, which introduces uncertainties in the error bars on cosmological parameters and also additional scatter in their best-fitting values. For future surveys, reducing both effects to an acceptable level requires an unfeasibly large number of simulations. In this paper we describe a way to expand the precision matrix around a covariance model and show how to estimate the leading order terms of this expansion from simulations. This is especially powerful if the covariance matrix is the sum of two contributions, C = A + B, where A is well understood analytically and can be turned off in simulations (e.g. shape noise for cosmic shear) to yield a direct estimate of B. We test our method in mock experiments resembling tomographic weak lensing data vectors from the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST). For DES we find that 400 N-body simulations are sufficient to achieve negligible statistical uncertainties on parameter constraints. For LSST this is achieved with 2400 simulations. The standard covariance estimator would require >105 simulations to reach a similar precision. We extend our analysis to a DES multiprobe case finding a similar performance. [ABSTRACT FROM AUTHOR]