Multi-Point Propagators in Cosmological Gravitational Instability

We introduce the concept of multi-point propagators between linear cosmic fields and their nonlinear counterparts in the context of cosmological perturbation theory. Such functions express how a non-linearly evolved Fourier mode depends on the full ensemble of modes in the initial density field. We identify and resum the dominant diagrams in the large-$k$ limit, showing explicitly that multi-point propagators decay into the nonlinear regime at the same rate as the two-point propagator. These analytic results generalize the large-$k$ limit behavior of the two-point propagator to arbitrary order. We measure the three-point propagator as a function of triangle shape in numerical simulations and confirm the results of our high-$k$ resummation. We show that any $n-$point spectrum can be reconstructed from multi-point propagators, which leads to a physical connection between nonlinear corrections to the power spectrum at small scales and higher-order correlations at large scales. As a first application of these results, we calculate the reduced bispectrum at one-loop in renormalized perturbation theory and show that we can predict the decrease in its dependence on triangle shape at redshift zero, when standard perturbation theory is least successful.Comment: 21 pages, 14 figures. Minor changes to match published version (Fig 11 changed, added reference

2-Point Moments in Cosmological Large Scale Structure: I. Theory and Comparison with Simulations

We present new perturbation theory (PT) predictions in the Spherical Collapse (SC) model for the 2-point moments of the large-scale distribution of dark matter density in the universe. We assume that these fluctuations grow under gravity from small Gaussian initial conditions. These predictions are compared with numerical simulations and with previous PT results to assess their domain of validity. We find that the SC model provides in practice a more accurate description of 2-point moments than previous tree-level PT calculations. The agreement with simulations is excellent for a wide range of scales (5-50 Mpc/h) and fluctuations amplitudes (0.02-2 variance). When normalized to unit variance these results are independent of the cosmological parameters and of the initial amplitude of fluctuations. The 2-point moments provide a convenient tool to study the statistical properties of gravitational clustering for fairly non-linear scales and complicated survey geometries, such as those probing the clustering of the Ly-alpha forest. In this context, the perturbative SC predictions presented here, provide a simple and novel way to test the gravitational instability paradigm.Comment: 10 LaTeX pages, 9 figs, submitted to MNRA

Resummed propagators in multi-component cosmic fluids with the eikonal approximation

We introduce the eikonal approximation to study the effect of the large-scale motion of cosmic fluids on their small-scale evolution. This approach consists in collecting the impact of the long-wavelength displacement field into a single or finite number of random variables, whose statistical properties can be computed from the initial conditions. For a single dark matter fluid, we show that we can recover the nonlinear propagators of renormalized perturbation theory. These are obtained with no need to assume that the displacement field follows the linear theory. Then we extend the eikonal approximation to many fluids. In particular, we study the case of two non-relativistic components and we derive their resummed propagators in the presence of isodensity modes. Unlike the adiabatic case, where only the phase of small-scale modes is affected by the large-scale advection field, the isodensity modes change also the amplitude on small scales. We explicitly solve the case of cold dark matter-baryon mixing and find that the isodensity modes induce only very small corrections to the resummed propagators.Comment: 18 pages, 9 figures, matches published version as PR

Constraints on Galaxy Bias, Matter Density, and Primordial Non--Gausianity from the PSCz Galaxy Redshift Survey

We compute the bispectrum for the \IRAS PSCz catalog and find that the galaxy distribution displays the characteristic signature of gravity. Assuming Gaussian initial conditions, we obtain galaxy biasing parameters $1/b_1=1.20^{+0.18}_{-0.19}$ and $b_2/b_1^2=-0.42\pm0.19$, with no sign of scale-dependent bias for $k\leq 0.3$ h/Mpc. These results impose stringent constraints on non-Gaussian initial conditions. For dimensional scaling models with $\chi^2_N$ statistics, we find N>49, which implies a constraint on primordial skewness $B_3<0.35$.Comment: 4 pages, 3 embedded figures, uses revtex style file, minor changes to reflect published versio

A Closure Theory for Non-linear Evolution of Cosmological Power Spectra

We apply a non-linear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop results of standard perturbation theory and beyond that, it is still capable of treating the non-linear evolution of matter power spectra. We find the exact integral expressions for the solutions of closure equations. These analytic expressions coincide with the renormalized one-loop results presented by Crocce & Scoccimarro (2006,2007). By constructing the non-linear propagator, we analytically evaluate the non-linear matter power spectra based on the first-order Born approximation of the integral expressions and compare it with those of the renormalized perturbation theory.Comment: 22 pages, 4 figures, accepted for publication in Ap

Generation of Vorticity and Velocity Dispersion by Orbit Crossing

We study the generation of vorticity and velocity dispersion by orbit crossing using cosmological numerical simulations, and calculate the backreaction of these effects on the evolution of large-scale density and velocity divergence power spectra. We use Delaunay tessellations to define the velocity field, showing that the power spectra of velocity divergence and vorticity measured in this way are unbiased and have better noise properties than for standard interpolation methods that deal with mass weighted velocities. We show that high resolution simulations are required to recover the correct large-scale vorticity power spectrum, while poor resolution can spuriously amplify its amplitude by more than one order of magnitude. We measure the scalar and vector modes of the stress tensor induced by orbit crossing using an adaptive technique, showing that its vector modes lead, when input into the vorticity evolution equation, to the same vorticity power spectrum obtained from the Delaunay method. We incorporate orbit crossing corrections to the evolution of large scale density and velocity fields in perturbation theory by using the measured stress tensor modes. We find that at large scales (k~0.1 h/Mpc) vector modes have very little effect in the density power spectrum, while scalar modes (velocity dispersion) can induce percent level corrections at z=0, particularly in the velocity divergence power spectrum. In addition, we show that the velocity power spectrum is smaller than predicted by linear theory until well into the nonlinear regime, with little contribution from virial velocities.Comment: 27 pages, 14 figures. v2: reorganization of the material, new appendix. Accepted by PR

Cosmological Simulations of Normal-Branch Braneworld Gravity

We introduce a cosmological model based on the normal branch of DGP braneworld gravity with a smooth dark energy component on the brane. The expansion history in this model is identical to LambdaCDM, thus evading all geometric constraints on the DGP cross-over scale r_c. This model can serve as a first approximation to more general braneworld models whose cosmological solutions have not been obtained yet. We study the formation of large scale structure in this model in the linear and non-linear regime using N-body simulations for different values of r_c. The simulations use the code presented in (F.S., arXiv:0905.0858) and solve the full non-linear equation for the brane-bending mode in conjunction with the usual gravitational dynamics. The brane-bending mode is attractive rather than repulsive in the DGP normal branch, hence the sign of the modified gravity effects is reversed compared to those presented in arXiv:0905.0858. We compare the simulation results with those of ordinary LambdaCDM simulations run using the same code and initial conditions. We find that the matter power spectrum in this model shows a characteristic enhancement peaking at k ~ 0.7 h/Mpc. We also find that the abundance of massive halos is significantly enhanced. Other results presented here include the density profiles of dark matter halos, and signatures of the brane-bending mode self-interactions (Vainshtein mechanism) in the simulations. Independently of the expansion history, these results can be used to place constraints on the DGP model and future generalizations through their effects on the growth of cosmological structure.Comment: 17 pages, 10 figures; v2: minor changes; v3: references added; v4: added appendix on comparison with previous results; matches published version; v5: corrected Eqs. (2.4-2.5) and Fig. 1 following Ref. [28]; all following results unchange