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We derive the Edgeworth streaming model (ESM) for the redshift space correlation function starting from an arbitrary distribution function for biased tracers of dark matter by considering its two-point statistics and show that it reduces to the Gaussian streaming model (GSM) when neglecting non- Gaussianities. We test the accuracy of the GSM and ESM independent of perturbation theory using the Horizon Run 2 A-body halo catalog. While the monopole of the redshift space halo correlation function is well described by the GSM, higher multipoles improve upon including the leading order non-Gaussian correction in the ESM: the GSM quadrupole breaks down on scales below 30 Mpc/h whereas the ESM stays accurate to 2% within statistical errors down to 10 Mpc/h. To predict the scale-dependent functions entering the streaming model we employ convolution Lagrangian perturbation theory (CLPT) based on the dust model and local Lagrangian bias. Since dark matter halos carry an intrinsic length scale given by their Lagrangian radius, we extend CLPT to the coarse-grained dust model and consider two different smoothing approaches operating in Eulerian and Lagrangian space, respectively. The coarse graining in Eulerian space features modified fluid dynamics different from dust while the coarse graining in Lagrangian space is performed in the initial conditions with subsequent single-streaming dust dynamics, implemented by smoothing the initial power spectrum in the spirit of the truncated Zel'dovich approximation. Finally, we compare the predictions of the different coarse-grained models for the streaming model ingredients to N-body measurements and comment on the proper choice of both the tracer distribution function and the smoothing scale. Since the perturbative methods we considered are not yet accurate enough on small scales, the GSM is sufficient when applied to perturbation theory. [ABSTRACT FROM AUTHOR]

We study the effect of coarse graining the dynamics of a pressureless self-gravitating fluid (coarsegrained dust) in the context of cosmological perturbation theory, in both the Eulerian and Lagrangian frameworks. We obtain recursion relations for the Eulerian perturbation kernels of the coarse-grained dust model by relating them to those of the standard pressureless fluid model. The effect of the coarse graining is illustrated by means of power and cross spectra for the density and velocity, which are computed up to oneloop order. In particular, the large-scale vorticity power spectrum that arises naUirally from a mass-weighted velocity is derived from first principles. We find qualitatively good agreement for the magnitude, shape, and spectral index of the vorticity power spectrum with recent measurements from N-body simulations and results from the effective field theory of large-scale structure. To lay the ground for applications in the context of Lagrangian perturbation theory, we finally describe how the kernels obtained in Eulerian space can be mapped to Lagrangian ones. [ABSTRACT FROM AUTHOR]

We investigate large-scale structure formation of collisionless dark matter in the phase space description based on the Vlasov (or collisionless Boltzmann) equation whose nonlinearity is induced solely by gravitational interaction according to the Poisson equation. Determining the time evolution of density and peculiar velocity demands solving the full Vlasov hierarchy for the moments of the phase space distribution function. In the presence of long-range interaction no consistent truncation of the hierarchy is known apart from the pressureless fluid (dust) model, which is incapable of describing virialization due to the occurrence of shell-crossing singularities and the inability to generate vorticity and higher cumulants like velocity dispersion. Our goal is to find a simple ansatz for the phase space distribution function that approximates the full Vlasov distribution function without pathologies in a controlled way and therefore can serve as theoretical TV-body double and as a replacement for the dust model. We argue that the coarse-grained Wigner probability distribution obtained from a wave function fulfilling the Schrödinger-Poisson equation (SPE) is the sought-after function. We show that its evolution equation approximates the Vlasov equation and therefore also the dust fluid equations before shell crossing, but cures the shell-crossing singularities and is able to describe regions of multistreaming and virialization. This feature was already employed in cosmological simulations of large-scale structure formation by Widrow and Kaiser (1993). The coarse-grained Wigner ansatz allows us to calculate all higher moments from density and velocity analytically, thereby incorporating nonzero higher cumulants in a self-consistent manner. On this basis we are able to show that the Schrödinger method automatically closes the corresponding hierarchy such that it suffices to solve the SPE in order to directly determine density and velocity and all higher cumulants. [ABSTRACT FROM AUTHOR]

We chart a path toward solving for the nonlinear gravitational dynamics of cold dark matter by relying on a semiclassical description using the propagator. The evolution of the propagator is given by a Schrödinger equation, where the small parameter ℏ acts as a softening scale that regulates singularities at shell-crossing. The leading-order propagator, called free propagator, is the semiclassical equivalent of the Zel'dovich approximation, that describes inertial particle motion along straight trajectories. At next-to-leading order, we solve for the propagator perturbatively and obtain, in the classical limit the displacement field from second-order Lagrangian perturbation theory (LPT). The associated velocity naturally includes an additional term that would be considered as third order in LPT. We show that this term is actually needed to preserve the underlying Hamiltonian structure, and ignoring it could lead to the spurious excitation of vorticity in certain implementations of second-order LPT. We show that for sufficiently small ℏ the corresponding propagator solutions closely resemble LPT, with the additions that spurious vorticity is avoided and the dynamics at shell-crossing is regularized. Our analytical results possess a symplectic structure that allows us to advance numerical schemes for the large-scale structure. For times shortly after shell-crossing, we explore the generation of vorticity, which in our method does not involve any explicit multistream averaging, but instead arises naturally as a conserved topological charge. [ABSTRACT FROM AUTHOR]

We calculate the halo correlation function in redshift space using the Gaussian streaming model (GSM). To determine the scale-dependent functions entering the GSM, we use local Lagrangian bias together with convolution Lagrangian perturbation theory (CLPT), which constitutes an approximation to the Post-Zel'dovich approximation. On the basis of N-body simulations, we demonstrate that a smoothing of the initial conditions with the Lagrangian radius improves the Zel'dovich approximation and its ability to predict the displacement field of protohalos. Based on this observation, we implement a "truncated" CLPT by smoothing the initial power spectrum and investigate the dependence of the streaming model ingredients on the smoothing scale. We find that the real space correlation functions of halos and their mean pairwise velocity are optimized if the coarse graining scale is chosen to be 1 Mpc/h at z=0, while the pairwise velocity dispersion is optimized if the smoothing scale is chosen to be the Lagrangian size of the halo. We compare theoretical results for the halo correlation function in redshift space to measurements within the Horizon run 2 N-body simulation halo catalog. We find that this simple two-filter smoothing procedure in the spirit of the truncated Zel'dovich approximation significantly improves the GSM+CLPT prediction of the redshift space halo correlation function over the whole mass range from large galaxy to galaxy cluster-sized halos. We expect that the necessity for two filter scales is an artifact of our local bias model, and that once a more physical bias model is implemented in CLPT, the only physically relevant smoothing scale will be related to the Lagrangian radius, in accord with our findings based on N-body simulations. [ABSTRACT FROM AUTHOR]