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We present an analytical description of the probability distribution function (PDF) of the smoothed 3D matter density field for modified gravity and dark energy. Our approach, based on the principles of Large Deviations Theory, is applicable to general extensions of the standard Lambda cold dark matter (ΛCDM) cosmology. We show that late-time changes to the law of gravity and background expansion can be included through Einstein-de Sitter spherical collapse dynamics combined with linear theory calculations and a calibration measurement of the non-linear variance of the smoothed density field from a simple numerical simulation. In a comparison to N -body simulations for f (R), DGP, and evolving dark energy theories, we find per cent level accuracy around the peak of the distribution for predictions in the mildly non-linear regime. A Fisher forecast of an idealized experiment with a Euclid -like survey volume demonstrates the power of combining measurements of the 3D matter PDF with the 3D matter power spectrum. This combination is shown to halve the uncertainty on parameters for an evolving dark energy model, relative to a power spectrum analysis on its own. The PDF is also found to substantially increase the detection significance for small departures from General Relativity, with improvements of up to six times compared to the power spectrum alone. This analysis is therefore very promising for future studies including non-Gaussian statistics, as it has the potential to alleviate the reliance of these analyses on expensive high-resolution simulations and emulators. [ABSTRACT FROM AUTHOR]

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]

Pinning down the total neutrino mass and the dark energy equation of state is a key aim for upcoming galaxy surveys. Weak lensing is a unique probe of the total matter distribution whose non-Gaussian statistics can be quantified by the one-point probability distribution function (PDF) of the lensing convergence. We calculate the convergence PDF on mildly nonlinear scales from first principles using large-deviation statistics, accounting for dark energy and the total neutrino mass. For the first time, we comprehensively validate the cosmology dependence of the convergence PDF model against large suites of simulated lensing maps, demonstrating its per cent level precision and accuracy. We show that fast simulation codes can provide highly accurate covariance matrices, which can be combined with the theoretical PDF model to perform forecasts and eliminate the need for relying on expensive N -body simulations. Our theoretical model allows us to perform the first forecast for the convergence PDF that varies the full set of ΛCDM parameters. Our Fisher forecasts establish that the constraining power of the convergence PDF compares favourably to the two-point correlation function for a Euclid-like survey area at a single source redshift. When combined with a cosmic microwave background prior from Planck, the PDF constrains both the neutrino mass M ν and the dark energy equation of state w 0 more strongly than the two-point correlation function. [ABSTRACT FROM AUTHOR]

We present a novel approach to generate higher order initial conditions (ICs) for cosmological simulations that take into account the distinct evolution of baryons and dark matter. We focus on the numerical implementation and the validation of its performance, based on both collisionless N -body simulations and full hydrodynamic Eulerian and Lagrangian simulations. We improve in various ways over previous approaches that were limited to first-order Lagrangian perturbation theory (LPT). Specifically, we (1) generalize n th-order LPT to multifluid systems, allowing 2LPT or 3LPT ICs for two-fluid simulations, (2) employ a novel propagator perturbation theory to set up ICs for Eulerian codes that are fully consistent with 1LPT or 2LPT, (3) demonstrate that our ICs resolve previous problems of two-fluid simulations by using variations in particle masses that eliminate spurious deviations from expected perturbative results, (4) show that the improvements achieved by going to higher order PT are comparable to those seen for single-fluid ICs, and (5) demonstrate the excellent (i.e. few per cent level) agreement between Eulerian and Lagrangian simulations, once high-quality initial conditions are used. The rigorous development of the underlying perturbation theory is presented in a companion paper. All presented algorithms are implemented in the monofonic music-2 package that we make publicly available. [ABSTRACT FROM AUTHOR]

The cosmic large-scale structure of our Universe is comprised of baryons and cold dark matter (CDM). Yet it is customary to treat these two components as a combined single-matter fluid with vanishing pressure, which is justified only for sufficiently large scales and late times. Here, we go beyond the single-fluid approximation and develop the perturbation theory for two gravitationally coupled fluids while still assuming vanishing pressure. We mostly focus on perturbative expansions in powers of D (or D +), the linear structure growth of matter in a ΛCDM Universe with cosmological constant Λ. We derive in particular (1) explicit recursion relations for the two fluid densities, (2) complementary all-order results in the Lagrangian-coordinates approach, as well as (3) the associated component wavefunctions in a semiclassical approach to cosmic large-scale structure. In our companion paper, we apply these new theoretical results to generate novel higher order initial conditions for cosmological hydrodynamical simulations. [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]

We comprehensively analyse the cosmology dependence of counts-in-cells statistics. We focus on the shape of the one-point probability distribution function (PDF) of the matter density field at mildly non-linear scales. Based on large-deviation statistics, we parametrize the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the non-linear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass M ν and can disentangle it from the clustering amplitude σ8. Using more than a million PDFs extracted from the Quijote simulations, we determine the response of the matter PDF to changing parameters in the νΛCDM model and successfully cross-validate the theoretical model and the simulation measurements. We present the first νΛCDM Fisher forecast for the matter PDF at multiple scales and redshifts, and its combination with the matter power spectrum. We establish that the matter PDF and the matter power spectrum are highly complementary at mildly non-linear scales. The matter PDF is particularly powerful for constraining the matter density Ωm, clustering amplitude σ8 and the total neutrino mass M ν. Adding the mildly non-linear matter PDF to the mildly non-linear matter power spectrum improves constraints on Ωm by a factor of 5 and σ8 by a factor of 2 when considering the three lowest redshifts. In our joint analysis of the matter PDF and matter power spectrum at three redshifts, the total neutrino mass is constrained to better than 0.01 eV with a total volume of 6 (Gpc h−1)3. We discuss how density-split statistics can be used to translate those encouraging results for the matter PDF into realistic observables in galaxy surveys. [ABSTRACT FROM AUTHOR]

Intensity mapping surveys will provide access to a coarse view of the cosmic large-scale structure at high redshifts. Given the large fraction of the sky that can be efficiently scanned using emission from cosmic neutral hydrogen (H  i), intensity mapping is ideally suited to probe a wide range of density environments and hence to constrain cosmology and fundamental physics. To efficiently extract information from 21 cm intensities beyond average, one needs non-Gaussian statistics that capture large deviations from the mean H  i density. Counts-in-cells are ideally suited for this purpose, as their statistics can be predicted accurately. We use a large state-of-the-art magnetohydrodynamic simulation from the IllustrisTNG project to determine the relation between neutral hydrogen and matter densities in cells. We demonstrate how our theoretical knowledge about the matter probability density function (PDF) for a given cosmology can be used to extract a parametrization-independent H  i bias function from a measured H  i PDF. Inspired by the shape of this bias function, we employ a simple quadratic approximation that reproduces the measured bias function at a few per cent level. Combining this quadratic bias function with the predicted matter PDF yields a fully predictive forward model for the H  i PDF that matches the measured H  i PDF at a few per cent accuracy at scale R = 5 Mpc  h −1 from redshift z = 5 to z = 1. Furthermore, we find a density-dependent H  i clustering signal that is consistent with theoretical expectations and could allow for joint constraints of H  i bias and the amplitude of matter fluctuations or the growth of structure. [ABSTRACT FROM AUTHOR]

We investigate large scale structure formation of collisionless dark matter in the phase space description based on the Vlasov-Poisson equation. We present the Schrödinger method, originally proposed by \cite{WK93} as numerical technique based on the Schrödinger Poisson equation, as an analytical tool which is superior to the common standard pressureless fluid model. Whereas the dust model fails and develops singularities at shell crossing the Schrödinger method encompasses multi-streaming and even virialization. [ABSTRACT FROM PUBLISHER]

The late universe contains a wealth of information about fundamental physics and gravity, wrapped up in non-Gaussian fields. To make use of as much information as possible, it is necessary to go beyond two-point statistics. Rather than going to higher-order N-point correlation functions, we demonstrate that the probability distribution function (PDF) of spheres in the matter field (a one-point function) already contains a significant amount of this non-Gaussian information. The matter PDF dissects different density environments which are lumped together in two-point statistics, making it particularly useful for probing modifications of gravity or expansion history. Our approach in Cataneo et al. 2021 extends the success of Large Deviation Theory for predicting the matter PDF in Λ CDM in these "extended" cosmologies. A Fisher forecast demonstrates the information content in the matter PDF via constraints for a Euclid-like survey volume combining the 3D matter PDF with the 3D matter power spectrum. Adding the matter PDF halves the uncertainties on parameters in an evolving dark energy model, relative to the power spectrum alone. Additionally, the matter PDF contains enough non-linear information to substantially increase the detection significance of departures from General Relativity, with improvements up to six times the power spectrum alone. This analysis demonstrates that the matter PDF is a promising non-Gaussian statistic for extracting cosmological information, particularly for beyond Λ CDM models. [ABSTRACT FROM AUTHOR]