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Journal ArticleDOI

Testing standard perturbation theory and the Eulerian local biasing scheme against N-body simulations

TL;DR: In this article, the Eulerian local bias model (ELB) was used to estimate the three-dimensional dark matter density field using standard perturbation theory (SPT) from the initial conditions of two high-resolution cosmological simulations.
Abstract: We test third-order standard perturbation theory (SPT) as an approximation to non-linear cosmological structure formation. A novel approach is used to numerically calculate the three-dimensional dark matter density field using SPT from the initial conditions of two high-resolution cosmological simulations. The calculated density field is compared to the non-linear dark matter field of the simulations both point-by-point and statistically. For smoothing scales above 8 Mpc/h it shows a good agreement up to redshift 0. We present a simple fitting formula to relate the linear and non-linear density contrast that accurately recovers the non-linear time evolution for 0 <= z <= 10 at the per cent level. To address the problem of biasing between the matter field and the haloes identified in the simulation, we employ the Eulerian local bias model (ELB), including non-linear bias up to the third order. The bias parameters are obtained by fitting a scatter plot of halo and matter density (both from the simulation and from SPT). Using these bias parameters, we can reconstruct the halo density field. We find that this reconstruction is not able to capture all the details of the halo distribution. We investigate how well the large scale bias can be described by a constant and if it corresponds to the linear bias parameter b_1 of the local bias model. We also discuss how well the halo-halo power spectrum and the halo-mass cross spectrum from the reconstructed halo density field agree with the corresponding statistics from the simulation. The results show that while SPT is an excellent approximation for the matter field for suitably large smoothing scales even at redshift 0, the ELB model can only account for some of the properties of the halo density field.
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TL;DR: In this paper, the authors use perturbation theory to predict the real-space pairwise halo velocity statistics and show that their model is accurate at the 2 per cent level only on scales s > 40 Mpc/h.
Abstract: Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for measuring the build-up of cosmological structure, which depends both on the expansion rate of the Universe and our theory of gravity. Galaxies occupy dark matter halos, whose redshift space clustering has a complex dependence on bias that cannot be inferred from the behavior of matter. We identify two distinct corrections on quasilinear scales (~ 30-80 Mpc/h): the non-linear mapping between real and redshift space positions, and the non-linear suppression of power in the velocity divergence field. We model the first non-perturbatively using the scale-dependent Gaussian streaming model, which we show is accurate at the 10 (s>25) Mpc/h for the monopole (quadrupole) halo correlation functions. We use perturbation theory to predict the real space pairwise halo velocity statistics. Our fully analytic model is accurate at the 2 per cent level only on scales s > 40 Mpc/h. Recent models that neglect the corrections from the bispectrum and higher order terms from the non-linear real-to-redshift space mapping will not have the accuracy required for current and future observational analyses. Finally, we note that our simulation results confirm the essential but non-trivial assumption that on large scales, the bias inferred from real space clustering of halos is the same one that determines their pairwise infall velocity amplitude at the per cent level.

218 citations

Journal ArticleDOI
TL;DR: In this paper , a comparison between the matter bispectrum derived with different flavors of perturbation theory at next-to-leading order and measurements from an unprecedentedly large suite of $N$-body simulations is made.
Abstract: We provide a comparison between the matter bispectrum derived with different flavours of perturbation theory at next-to-leading order and measurements from an unprecedentedly large suite of $N$-body simulations. We use the $\chi^2$ goodness-of-fit test to determine the range of accuracy of the models as a function of the volume covered by subsets of the simulations. We find that models based on the effective-field-theory (EFT) approach have the largest reach, standard perturbation theory has the shortest, and `classical' resummed schemes lie in between. The gain from EFT, however, is less than in previous studies. We show that the estimated range of accuracy of the EFT predictions is heavily influenced by the procedure adopted to fit the amplitude of the counterterms. For the volumes probed by galaxy redshift surveys, our results indicate that it is advantageous to set three counterterms of the EFT bispectrum to zero and measure the fourth from the power spectrum. We also find that large fluctuations in the estimated reach occur between different realisations. We conclude that it is difficult to unequivocally define a range of accuracy for the models containing free parameters. Finally, we approximately account for systematic effects introduced by the $N$-body technique either in terms of a scale- and shape-dependent bias or by boosting the statistical error bars of the measurements (as routinely done in the literature). We find that the latter approach artificially inflates the reach of EFT models due to the presence of tunable parameters.

9 citations

Journal ArticleDOI
TL;DR: In this article , the grid-based method to compute the nonlinear density and velocity fields in standard perturbation theory (SPT) from a given linear power spectrum has been presented by taking the redshift-space distortions into account.
Abstract: Perturbation theory (PT) has been used to interpret the observed nonlinear large-scale structure statistics at the quasi-linear regime. To facilitate the PT-based analysis, we have presented the GridSPT algorithm, a grid-based method to compute the nonlinear density and velocity fields in standard perturbation theory (SPT) from a given linear power spectrum. Here, we further put forward the approach by taking the redshift-space distortions into account. With the new implementation, we have, for the first time, generated the redshift-space density field to the fifth order and computed the next-to-next-to-leading order (2 loop) power spectrum and the next-to-leading order (1 loop) bispectrum of matter clustering in redshift space. By comparing the result with corresponding analytical SPT calculation and $N$-body simulations, we find that the SPT calculation (A) suffers much more from the UV sensitivity due to the higher-derivative operators and (B) deviates from the $N$-body results from the Fourier wavenumber smaller than real space $k_{\rm max}$. Finally, we have shown that while Pad\'e approximation removes spurious features in morphology, it does not improve the modeling of power spectrum and bispectrum.

4 citations

Journal ArticleDOI
TL;DR: In this paper , a non-parametric Lagrangian biasing model was proposed to fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at $z=0.5.
Abstract: We present a non-parametric Lagrangian biasing model and fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at $z=0.5$. Unlike the perturbative halo bias model widely used in interpreting the observed large-scale structure traced by galaxies, we find a non-negative halo-to-mass ratio that increases monotonically with the linear overdensity $\delta_1$ in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may give rising halo number counts at negative overdensities. The shape of the halo-to-mass ratio is unlikely to be described by a polynomial of $\delta_1$ and other quantities. Especially for massive halos with $6\times10^{12}\ h^{-1}\ M_\odot$, the halo-to-mass ratio starts soaring up at $\delta_1>0$, substantially different from the predictions of the bias expansion. We show that for the halo masses we consider ($M>3\times10^{11}\ h^{-1}\ M_\odot$) a non-parametric halo-to-mass ratio as a function of $\delta_1$ and its local derivative $ abla^2\delta_1$ can recover the halo power spectra to sub-percent level for wavenumbers $k=0.01-0.1\ h\ {\rm Mpc}^{-1}$ given a proper smoothing scale to filter the initial density field, even though we do not fit the power spectrum directly. However, there is mild dependence of the recovery of the halo power spectrum on the smoothing scale and other input parameters. At $k<0.01\ h\ {\rm Mpc}^{-1}$ and for massive halos with $M>6\times10^{12}\ h^{-1}\ M_\odot$, our non-parametric model leads to a few percent overestimation of the halo power spectrum, indicating the need for larger or multiple smoothing scales. The halo-to-mass ratios obtained qualitatively agree with intuitions from extended Press-Schechter theory. We compare our framework to the bias expansion and discuss possible extensions.

2 citations