Nonlinear Evolution Of Large-scale Structure Research Articles

CMB weak-lensing beyond the Born approximation: a numerical approach

We perform a complete study of the gravitational lensing effect beyond the Born approximation on the Cosmic Microwave Background (CMB) anisotropies using a multiple-lens raytracing technique through cosmological N-body simulations of the DEMNUni suite. The impact of second-order effects accounting for the non-linear evolution of large-scale structures is evaluated propagating for the first time the full CMB lensing jacobian together with the light rays trajectories. We carefully investigate the robustness of our approach against several numerical effects in the raytracing procedure and in the N-body simulation itself, and find no evidence of large contaminations. We discuss the impact of beyond-Born corrections on lensed CMB observables, and compare our results with recent analytical predictions that appeared in the literature, finding a good agreement, and extend these results to smaller angular scales. We measure the gravitationally-induced CMB polarization rotation that appears in the geodesic equation at second order, and compare this result with the latest analytical predictions. We then present the detection prospect of beyond-Born effects with the future CMB-S4 experiment. We show that corrections to the temperature power spectrum can be measured only if a good control of the extragalactic foregrounds is achieved. Conversely, the beyond-Born corrections on E and B-modes power spectra will be much more difficult to detect.

Iterative initial condition reconstruction

Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift $z=0$, we find that after eight iterations the reconstructed density is more than $95\%$ correlated with the initial density at $k\le 0.35\; h\mathrm{Mpc}^{-1}$. The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at $k\le 0.2\; h\mathrm{Mpc}^{-1}$, and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2-3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at $z=0$ and by a factor of 2.5 at $z=0.6$, improving standard BAO reconstruction by $70\%$ at $z=0$ and $30\%$ at $z=0.6$, and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.

AN APPLICATION OF THE WIENER HERMITE EXPANSION TO THE NONLINEAR EVOLUTION OF DARK MATTER

We apply the Wiener Hermite (WH) expansion to the non-linear evolution of Large-Scale Structure, and obtain an approximate expression for the matter power spectrum in full order of the expansion. This method allows us to expand any random function in terms of an orthonormal bases in space of random functions in such a way that the first order of the expansion expresses the Gaussian distribution, and others are the deviation from the Gaussianity. It is proved that the Wiener Hermite expansion is mathematically equivalent with the $\Gamma$-expansion approach in the Renormalized Perturbation Theory (RPT). While an exponential behavior in the high-$k$ limit has been proved for the mass density and velocity fluctuations of Dark Matter in the RPT, we reprove the behavior in the context of the Wiener Hermite expansion using the result of Standard Perturbation Theory (SPT). We propose a new approximate expression for the matter power spectrum which interpolates the low-$k$ expression corresponding to 1-loop level in SPT and the high-$k$ expression obtained by taking a high-$k$ limit of the WH expansion. The validity of our prescription is specifically verified by comparing with the 2-loop solutions of the SPT. The proposed power spectrum agrees with the result of $N$-body simulation with the accuracy better than 1% or 2% in a range of the BAO scales, where the wave number is about $k= 0.2 \sim 0.4$ $h{\rm Mpc^{-1}}$ at $z=0.5-3.0$. This accuracy is comparable to or slightly less than the ones in the Closure Theory whose the fractional difference from N body result is within 1%. A merit of our method is that the computational time is very short because only single and double integrals are involved in our solution.

Galaxy clustering constraints on deviations from Newtonian gravity at cosmological scales. II. Perturbative and numerical analyses of power spectrum and bispectrum

We explore observational constraints on possible deviations from Newtonian gravity by means of large-scale clustering of galaxies. We measure the power spectrum and the bispectrum of Sloan Digital Sky Survey galaxies and compare the result with predictions in an empirical model of modified gravity. Our model assumes an additional Yukawa-like term with two parameters that characterize the amplitude and the length scale of the modified gravity. The model predictions are calculated using two methods; second-order perturbation theory and direct $N$-body simulations. These methods allow us to study nonlinear evolution of large-scale structure. Using the simulation results, we find that perturbation theory provides reliable estimates for the power spectrum and the bispectrum in the modified Newtonian model. We also construct mock galaxy catalogs from the simulations, and derive constraints on the amplitude and the length scale of deviations from Newtonian gravity. The resulting constraints from the power spectrum are consistent with those obtained in our earlier, indicating the validity of the previous empirical modeling of gravitational nonlinearity in the modified Newtonian model. If linear biasing is adopted, the bispectrum of the Sloan Digital Sky Survey galaxies yields constraints very similar to those from the power spectrum. If we allow for the nonlinear biasing instead, we find that the ratio of the quadratic to linear biasing coefficients, ${b}_{2}/{b}_{1}$, should satisfy $\ensuremath{-}0.25<{b}_{2}/{b}_{1}<0.19$ for $\ensuremath{\lambda}=5{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ and $\ensuremath{-}0.19<{b}_{2}/{b}_{1}<0.13$ for $\ensuremath{\lambda}=10{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ in the modified Newtonian model.

On Local Approximations to the Nonlinear Evolution of Large‐Scale Structure

We present a comparative analysis of several methods, known as local Lagrangian approximations, which are aimed to the description of the nonlinear evolution of large-scale structure. We have investigated various aspects of these approximations, such as the evolution of a homogeneous ellipsoid, collapse time as a function of initial conditions, and asymptotic behavior. As one of the common features of the local approximations, we found that the calculated collapse time decreases asymptotically with the inverse of the initial shear. Using these approximations, we have computed the cosmological mass function, finding reasonable agreement with N-body simulations and the Press-Schechter formula.

Weak Gravitational Lensing Bispectrum

Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters that govern them. The nonlinear evolution of large-scale structure produces a non-Gaussian signal that is potentially observable in galaxy shear data. We study the three-point statistics of the convergence, specifically the bispectrum, using the dark matter halo approach, which describes the density field in terms of correlations between and within dark matter halos. Our approach allows us to study the effect of the mass distribution in observed fields, in particular the bias induced by the lack of rare massive halos (clusters) in observed fields. We show that the convergence skewness is primarily due to rare and massive dark matter halos, with skewness converging to its mean value only if halos of mass M > 1015 M☉ are present. This calculational method can in principle be used to correct for such a bias as well as to search for more robust statistics related to the two- and three-point correlations.

Linear Evolution of the Gravitational Potential: A New Approximation for the Nonlinear Evolution of Large-Scale Structure

Using a full nonlinear numerical gravitational clustering simulation with Ω=1 cold dark matter and Zel'dovich initial conditions, we show that the gravitational potential evolves very little up to the present on length scales≥1.25 h -1 Mpc. We present a new approximation for the nonlinear evolution of large-scale structure, in which the gravitational potential field is assumed to remain constant up to the present, but the matter obeys the usual nonlinear equations of motion in this potential field

Nonlinear evolution of large-scale structure in the universe

Using N-body simulations we study the nonlinear development of primordial density perturbation in an Einstein--de Sitter universe. We compare the evolution of an initial distribution without small-scale density fluctuations to evolution from a random Poisson distribution. These initial conditions mimic the assumptions of the adiabatic and isothermal theories of galaxy formation. The large-scale structures which form in the two cases are markedly dissimilar. In particular, the correlation function xi(r) and the visual appearance of our adiabatic (or ''pancake'') models match better the observed distribution of galaxies. This distribution is characterized by large-scale filamentary structure. Because the pancake models do not evolve in a self-similar fashion, the slope of xi(r) steepens with time; as a result there is a unique epoch at which these models fit the galaxy observations. We find the ratio of cutoff length to correlation length at this time to be lambda/sub min//r/sub 0/ = 5.1; its expected value in a neutrino dominated universe is 4(..cap omega..h)/sup -1/ (H/sub 0/ = 100h km s/sup -1/ Mpc/sup -1/). At early epochs these models predict a negligible amplitude for xi(r) and could explain the lack of measurable clustering in the Ly..cap alpha.. absorption lines of high-redshift quasars. However, large-scale structuremore » in our models collapses after z = 2. If this collapse precedes galaxy formation as in the usual pancake theory, galaxies formed uncomfortably recently. The extent of this problem may depend on the cosmological model used; the present series of experiments should be extended in the future to include models with ..cap omega..<1.« less