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We present a detailed description and validation of our massively parallel update to the mass-Peak Patch method, a fully predictive initial-space algorithm to quickly generate dark matter halo catalogues in very large cosmological volumes. We perform an extensive systematic comparison to a suite of N -body simulations covering a broad range of redshifts and simulation resolutions, and find that, without any parameter fitting, our method is able to generally reproduce N -body results while typically using over 3 orders of magnitude less CPU time, and a fraction of the memory cost. Instead of calculating the full non-linear gravitational collapse determined by an N -body simulation, the mass-Peak Patch method finds an overcomplete set of just-collapsed structures around a hierarchy of density-peak points by coarse-grained (homogeneous) ellipsoidal dynamics. A complete set of mass peaks, or haloes, is then determined by exclusion of overlapping patches, and second-order Lagrangian displacements are used to move the haloes to their final positions and to give their flow velocities. Our results show that the mass-Peak Patch method is well suited for creating large ensembles of halo catalogues to mock cosmological surveys, and to aid in complex statistical interpretations of cosmological models. [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]