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We present the merging of the Particle-Mesh (PM) relativistic gevolution code with the TreePM gadget-4 code, with the aim of studying general relativity effects in cosmology. Our code, called grgadget , is able to track the evolution of metric perturbations in the weak field limit by using gevolution 's implementation of a relativistic PM in the Poisson gauge. To achieve this, starting from gevolution , we have written a c++ library called libgevolution , which allows a code to access and use the same abstractions and resources that gevolution uses for its PM-only N -body simulations. The code works under the assumption that particle interactions at short distances can be approximated as Newtonian, so that we can combine the forces computed with a Newtonian Tree with those computed with a relativistic PM. The result is a TreePM simulation code that represents metric perturbations at the scales where they are relevant while resolving non-linear structures. We validate our code by closely matching gadget-4 forces, computed with the Tree switched off, with those computed with libgevolution in the Newtonian limit. With grgadget , we obtain a matter power spectrum that is compatible with Newtonian gadget-4 at small scales and contains GR features at large scales that are consistent with results obtained with gevolution. We demonstrate that, due to the better resolution of the highly non-linear regime, the representation of the relativistic fields sampled on the mesh improves with respect to the PM-only simulations. [ABSTRACT FROM AUTHOR]

We present a perturbative treatment of non-linear galaxy clustering in the context of the cubic Galileon modified gravity model, in terms of second-order Lagrangian Perturbation theory and an extension of ellipsoidal collapse that includes Vainshtein screening. We numerically implement such prescriptions in the approximate pinocchio code, and use it to generate realizations of the matter density field and halo catalogues with different prescriptions for ellipsoidal collapse. We investigate the impact of three different approximations in the computation of collapse times on the halo mass function, halo bias, and matter power spectrum. In the halo mass function, both the modified gravity effect and the screening effect are significant in the high-mass end, similar to what is found for other MG models. We perform a comparison with N -body simulations to assess the validity of our approach, and show that we can reproduce the same trend observed in simulations for all quantities considered. With a simple modification to the grouping algorithm of pinocchio to take into account the gravity modification, and without the need to re-calibrate the algorithm, we show that we can reproduce the linear halo bias and the mildly non-linear matter power spectrum of simulations with good accuracy, especially for the implementation with Vainshtein screening. We stress that, while approximate, our method is orders of magnitude faster than a full N -body simulation, making it an optimal tool for the quick generation of large sets of halo catalogues for cosmological observables. [ABSTRACT FROM AUTHOR]

We investigate the accuracy of weak lensing simulations by comparing the results of five independently developed lensing simulation codes run on the same input N -body simulation. Our comparison focuses on the lensing convergence maps produced by the codes, and in particular on the corresponding PDFs, power spectra, and peak counts. We find that the convergence power spectra of the lensing codes agree to |$\lesssim 2{{\ \rm per\ cent}}$| out to scales ℓ ≈ 4000. For lensing peak counts, the agreement is better than |$5{{\ \rm per\ cent}}$| for peaks with signal-to-noise ≲ 6. We also discuss the systematic errors due to the Born approximation, line-of-sight discretization, particle noise, and smoothing. The lensing codes tested deal in markedly different ways with these effects, but they none-the-less display a satisfactory level of agreement. Our results thus suggest that systematic errors due to the operation of existing lensing codes should be small. Moreover their impact on the convergence power spectra for a lensing simulation can be predicted given its numerical details, which may then serve as a validation test. [ABSTRACT FROM AUTHOR]

We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constraints related to growth rate of structure, Alcock–Paczynski distortions, and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE–COLA, pinocchio, and peakpatch), methods that rely on halo assignment schemes on to dark matter overdensities calibrated with a target N-body run (halogen, patchy), and two standard assumptions about the full density probability distribution function (Gaussian and lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within |$5{{\ \rm per\ cent}}$|⁠, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within |$10{{\ \rm per\ cent}}$|⁠. Overall, we find that covariances built from approximate simulations yield errors on model parameters within |$10{{\ \rm per\ cent}}$| of those from the N-body-based covariance. [ABSTRACT FROM AUTHOR]

We compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogues to the same quantities obtained from full N -body simulations. To this purpose we employ a large set of 300 realizations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and non-linear bias parameters depends on the approximate method used for the determination of the bispectrum variance. As general result, most methods provide errors within 10 per cent of the errors estimated from N -body simulations. Exceptions are those methods requiring calibration of the clustering amplitude but restrict this to 2-point statistics. Finally we test how our results are affected by being limited to a few hundreds measurements from N -body simulation by comparing with a larger set of several thousands of realizations performed with one approximate method. [ABSTRACT FROM AUTHOR]

This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic two-point correlation function measurements. Our comparison includes seven approximate methods, which can be divided into three categories: predictive methods that follow the evolution of the linear density field deterministically (ice-cola, peak patch, and pinocchio), methods that require a calibration with N -body simulations (patchy and halogen), and simpler recipes based on assumptions regarding the shape of the probability distribution function (PDF) of density fluctuations (lognormal and Gaussian density fields). We analyse the impact of using covariance estimates obtained from these approximate methods on cosmological analyses of galaxy clustering measurements, using as a reference the covariances inferred from a set of full N -body simulations. We find that all approximate methods can accurately recover the mean parameter values inferred using the N -body covariances. The obtained parameter uncertainties typically agree with the corresponding N -body results within 5 per cent for our lower mass threshold and 10 per cent for our higher mass threshold. Furthermore, we find that the constraints for some methods can differ by up to 20 per cent depending on whether the halo samples used to define the covariance matrices are defined by matching the mass, number density, or clustering amplitude of the parent N -body samples. The results of our configuration-space analysis indicate that most approximate methods provide similar results, with no single method clearly outperforming the others. [ABSTRACT FROM AUTHOR]

We present a comparison of major methodologies of fast generating mock halo or galaxy catalogues. The comparison is done for two-point (power spectrum and two-point correlation function in real and redshift space), and the three-point clustering statistics (bispectrum and three-point correlation function). The reference catalogues are drawn from the BigMultiDark N-body simulation. Both friend-of-friends (including distinct haloes only) and spherical over-density (including distinct haloes and subhalos) catalogues have been used with the typical number density of a large volume galaxy surveys. We demonstrate that a proper biasing model is essential for reproducing the power spectrum at quasi-linear and even smaller scales. With respect to various clustering statistics, a methodology based on perturbation theory and a realistic biasing model leads to very good agreement with N-body simulations. However, for the quadrupole of the correlation function or the power spectrum, only the method based on semi-N-body simulation could reach high accuracy (1 per cent level) at small scales, i.e. r < 25 h-1 Mpc or k > 0.15 h Mpc-1. Full N-body solutions will remain indispensable to produce reference catalogues. Nevertheless, we have demonstrated that the more efficient approximate solvers can reach a few per cent accuracy in terms of clustering statistics at the scales interesting for the large-scale structure analysis. This makes them useful for massive production aimed at covariance studies, to scan large parameter spaces, and to estimate uncertainties in data analysis techniques, such as baryon acoustic oscillation reconstruction, redshift distortion measurements, etc. [ABSTRACT FROM AUTHOR]