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When constructing galaxy mock catalogs based on suits of dark matter halo catalogs generated with approximated, calibrated or machine-learning approaches, the assignment of intrinsic properties for such tracers is a step of paramount relevance, given that these can shape the abundance of mock galaxy cluster and the spatial distribution of mock galaxies. We explore the possibility to assign properties of dark matter halos within the context of calibrated/learning approaches, explicitly using clustering information. The goal is to retrieve the correct signal of primary and secondary large-effective bias as a function of properties reconstructed solely based on phase-space properties of the halo distribution and dark matter density field. The algorithm reconstructs a set halo properties (such as virial mass, maximum circular velocity, concentration and spin) constraint to reproduce both primary and secondary (or assembly) bias. The key ingredients of the algorithm are the implementation of individually-assigned large-scale effective bias, a multi-scale approach to account for halo exclusion and a hierarchical assignment of halo properties. The method facilitates the assignment of halo properties aiming at replicating the large-scale effective bias, both primary and secondary. This improves over over previous methods found in the literature, especially at the high mass population. We have designed an strategy to reconstruct the main properties of dark matter halos obtained by calibrated/learning algorithms, in a way that the expected one and two-point statistics (on large scales) replicates the signal from detailed N-body simulations. We encourage the application of this strategy (or the implementation of our algorithm) for the generation of mock catalogs of dark matter halos based on approximated methods., Comment: 9 Pages, 4 Figures. Submitted to A&A. Comments welcome

We assess the effectiveness of a non-parametric bias model in generating mock halo catalogues for modified gravity (MG) cosmologies, relying on the distribution of dark matter from either MG or $\Lambda$CDM. We aim to generate halo catalogues that effectively capture the distinct impact of MG, ensuring high accuracy in both two- and three-point statistics for comprehensive analysis of large-scale structures. As part of this study we aim at investigating the inclusion of MG into non-local bias to directly map the tracers onto $\Lambda$CDM fields, which would save many computational costs. We employ the bias assignment method (BAM) to model halo distribution statistics by leveraging seven high-resolution COLA simulations of MG cosmologies. Taking into account cosmic-web dependencies when learning the bias relations, we design two experiments to map the MG effects: one utilising the consistent MG density fields and the other employing the benchmark $\Lambda$CDM density field. BAM generates MG halo catalogues from both calibrations experiments excelling in summary statistics, achieving a $\sim 1\%$ accuracy in the power spectrum across a wide range of $k$-modes, with only minimal differences well below 10\% at modes subject to cosmic variance, particularly below $k<0.07$ $h$Mpc$^{-1}$. The reduced bispectrum remains consistent with the reference catalogues within 10\% for the studied configuration. Our results demonstrate that a non-linear and non-local bias description can model the effects of MG starting from a $\Lambda$CDM dark matter field., Comment: 15 pages, 10 figures, 2 tables

We measure the signal of secondary halo bias as a function of a variety of intrinsic and environmental halo properties, and characterize its statistical significance as a function of cosmological redshift. Using fixed and paired $N$-body simulations of dark-matter halos -- the UNIT simulation -- with masses above $10^{11}M_{\odot}h^{-1}$ identified over a wide range of cosmological redshifts (0

We present an improved analytical model to predict the Lyman-alpha forest at the field level in redshift space from the dark matter field, expanding upon the widely-used Fluctuating Gunn-Peterson approximation (FGPA). In particular, we introduce the dependence on the cosmic web environment (knots, filaments, sheets, voids) in the model, thereby effectively accounting for non-local bias. Furthermore, we include a detailed treatment of velocity bias in the redshift space distortions modelling, allowing the velocity bias to be cosmic-web dependent. We find evidence for a significant difference of the same model parameters in different environments, suggesting that for the investigated setup the simple standard FGPA is not able to adequately predict the Lyman-alpha forest in the different cosmic web regimes. We reproduce the summary statistics of the reference cosmological hydrodynamic simulation we use for comparison, yielding accurate mean transmitted flux, probability distribution function, 3D power spectrum, and bispectrum. In particular, we achieve maximum deviation and average deviations accuracy in the Lyman-alpha forest 3D power spectrum of $\sim 3\%$ and $\sim 0.1\%$ up to $k\sim 0.4 \, h \, {\rm Mpc}^{-1}$, $\sim 5\%$ and $\sim 1.8\%$ up to $k \sim 1.4 \, h \, {\rm Mpc}^{-1}$. Our new model outperforms previous analytical efforts to predict the Lyman-alpha forest at the field level in all the probed summary statistics, and has the potential to become instrumental in the generation of fast accurate mocks for covariance matrices estimation in the context of current and forthcoming Lyman-alpha forest surveys., Comment: 15 pages, 7 figures, 2 tables. Accepted for publication in A&A

We present a novel approach to the construction of mock galaxy catalogues for large-scale structure analysis based on the distribution of dark matter halos obtained with effective bias models at the field level. We aim to produce mock galaxy catalogues capable of generating accurate covariance matrices for a number of cosmological probes that are expected to be measured in current and forthcoming galaxy redshift surveys (e.g. two- and three-point statistics). We use the bias assignment method (BAM) to model the statistics of halo distribution through a learning algorithm using a few detailed $N$-body simulations, and approximated gravity solvers based on Lagrangian perturbation theory. Using specific models of halo occupation distributions, we generate galaxy mocks with the expected number density and central-satellite fraction of emission-line galaxies, which are a key target of the DESI experiment. BAM generates mock catalogues with per cent accuracy in a number of summary statistics, such as the abundance, the two- and three-point statistics of halo distributions, both in real and redshift space. In particular, the mock galaxy catalogues display $\sim 3\%-10\%$ accuracy in the multipoles of the power spectrum up to scales of $k\sim 0.4\,h^{-1}{\rm Mpc}$. We show that covariance matrices of two- and three-point statistics obtained with BAM display a similar structure to the reference simulation. BAM offers an efficient way to produce mock halo catalogues with accurate two- and three-point statistics, and is able to generate a variety of multi-tracer catalogues with precise covariance matrices of several cosmological probes. We discuss future developments of the algorithm towards mock production in DESI and other galaxy-redshift surveys. (Abridged), Comment: Accepted for publication at A&A

This work presents a new physically-motivated supervised machine learning method, Hydro-BAM, to reproduce the three-dimensional Lyman-$\alpha$ forest field in real and in redshift space learning from a reference hydrodynamic simulation, thereby saving about 7 orders of magnitude in computing time. We show that our method is accurate up to $k\sim1\,h\,\rm{Mpc}^{-1}$ in the one- (PDF), two- (power-spectra) and three-point (bi-spectra) statistics of the reconstructed fields. When compared to the reference simulation including redshift space distortions, our method achieves deviations of $\lesssim2\%$ up to $k=0.6\,h\,\rm{Mpc}^{-1}$ in the monopole, $\lesssim5\%$ up to $k=0.9\,h\,\rm{Mpc}^{-1}$ in the quadrupole. The bi-spectrum is well reproduced for triangle configurations with sides up to $k=0.8\,h\,\rm{Mpc}^{-1}$. In contrast, the commonly-adopted Fluctuating Gunn-Peterson approximation shows significant deviations already neglecting peculiar motions at configurations with sides of $k=0.2-0.4\,h\,\rm{Mpc}^{-1}$ in the bi-spectrum, being also significantly less accurate in the power-spectrum (within 5$\%$ up to $k=0.7\,h\,\rm{Mpc}^{-1}$). We conclude that an accurate analysis of the Lyman-$\alpha$ forest requires considering the complex baryonic thermodynamical large-scale structure relations. Our hierarchical domain specific machine learning method can efficiently exploit this and is ready to generate accurate Lyman-$\alpha$ forest mock catalogues covering large volumes required by surveys such as DESI and WEAVE., Comment: Accepted for publication by ApJ

This paper investigates the hierarchy of baryon physics assembly bias relations obtained from state-of-the-art hydrodynamic simulations with respect to the underlying cosmic web spanned by the dark matter field. Using the Bias Assignment Method (BAM) we find that non-local bias plays a central role. We classify the cosmic web based on the invariants of the curvature tensor defined not only by the gravitational potential, but especially by the over-density, as small scale clustering becomes important in this context. First, the gas density bias relation can be directly mapped onto the dark matter density field to high precision exploiting the strong correlation between them. In a second step, the neutral hydrogen is mapped based on the dark matter and the gas density fields. Finally, the temperature is mapped based on the previous quantities. This permits us to statistically reconstruct the baryon properties within the same simulated volume finding percent-precision in the two-point statistics and compatible results in the three-point statistics, in general within 1-$\sigma$, with respect to the reference simulation (with 5 to 6 orders of magnitude less computing time). This paves the path to establish the best set-up for the construction of mocks probing the intergalactic medium for the generation of such key ingredients in the statistical analysis of large forthcoming missions such as DESI, Euclid, J-PAS and WEAVE., Comment: Accepted for publication by ApJ

This work investigates the connection between the cosmic web and the halo distribution through the gravitational potential at the field level. We combine three fields of research, cosmic web classification, perturbation theory expansions of the halo bias, and halo (galaxy) mock catalogue making methods. In particular, we use the invariants of the tidal field and the velocity shear tensor as generating functions to reproduce the halo number counts of a reference catalogue from full gravity calculations, populating the dark matter field on a mesh well into the non-linear regime ($3\,h^{-1}\,{\rm Mpc}$ scales). Our results show an unprecedented agreement with the reference power spectrum within 1% up to $k=0.72\,h\,{\rm Mpc}^{-1}$. By analysing the three-point statistics on large scales (configurations of up to $k=0.2\,h\,{\rm Mpc}^{-1}$), we find evidence for non-local bias at the 4.8 $\sigma$ confidence level, being compatible with the reference catalogue. In particular, we find that a detailed description of tidal anisotropic clustering on large scales is crucial to achieve this accuracy at the field level. These findings can be particularly important for the analysis of the next generation of galaxy surveys in mock galaxy production., Comment: 19 pages, 10 figures and 2 tables, accepted for publication at MNRAS

In this paper we demonstrate that the information encoded in \emph{one} single (sufficiently large) $N$-body simulation can be used to reproduce arbitrary numbers of halo catalogues, using approximated realisations of dark matter density fields with different initial conditions. To this end we use as a reference one realisation (from an ensemble of $300$) of the Minerva $N$-body simulations and the recently published Bias Assignment Method to extract the local and non-local bias linking the halo to the dark matter distribution. We use an approximate (and fast) gravity solver to generate $300$ dark matter density fields from the down-sampled initial conditions of the reference simulation and sample each of these fields using the halo-bias and a kernel, both calibrated from the arbitrarily chosen realisation of the reference simulation. We show that the power spectrum, its variance and the three-point statistics are reproduced within $\sim 2\%$ (up to $k\sim1.0\,h\,{\rm Mpc}^{-1}$), $\sim 5-10\%$ and $\sim 10\%$, respectively. Using a model for the real space power spectrum (with three free bias parameters), we show that the covariance matrices obtained from our procedure lead to parameter uncertainties that are compatible within $\sim 10\%$ with respect to those derived from the reference covariance matrix, and motivate approaches that can help to reduce these differences to $\sim 1\%$. Our method has the potential to learn from one simulation with moderate volumes and high-mass resolution and extrapolate the information of the bias and the kernel to larger volumes, making it ideal for the construction of mock catalogues for present and forthcoming observational campaigns such as Euclid or DESI., Comment: Accepted for publication at MNRAS

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 catalogs to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of three-hundred realisations 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 nonlinear bias parameters depends on the approximate method used for the determination of the bispectrum variance. As general result, most methods provide errors within 10% of the errors estimated from N-body simulations. Exceptions are those methods requiring calibration of the clustering amplitude but restrict this to two-point statistics. Finally we test how our results are affected by being limited to a few hundreds measurements from N-body simulation, and therefore to the bispectrum variance, by comparing with a larger set of several thousands realisations performed with one approximate method., Comment: Additional results with respect to v1, new section and new figures added. 25 pages, 1 table 18 figures

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 constrains 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 onto dark-matter overdensities calibrated with a target N-body run (Halogen, Patchy) and two standard assumptions about the full density PDF (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 $5\%$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10\%$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10\%$ of those from the N-body based covariance., Comment: 20 pages, 16 figures, replaced to match accepted MNRAS version. Results on parameter errors changed

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 (log-normal 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% for our lower mass threshold, and 10% for our higher mass threshold. Furthermore, we find that the constraints for some methods can differ by up to 20% 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., Comment: 23 pages, 11 figures. Replaced to match accepted MNRAS version. Included Kullback-Leibler divergence

We aim to quantify the capability of the inhomogeneous distribution of galaxy clusters, represented by the two-point statistics in Fourier space, to retrieve information on the underlying scaling relations. We make a case study using the mass X-ray luminosity scaling relation for galaxy clusters and study its impact on the clustering pattern of these objects. We define the luminosity-weighted power spectrum and introduce the luminosity power spectrum as direct assessment of the clustering of the property of interest, in our case, the cluster X-ray luminosity. Using a suite of halo catalogs extracted from N-body simulations and realistic estimates of the mass X-ray luminosity relation, we measured these statistics with their corresponding covariance matrices. By carrying out a Fisher matrix analysis, we quantified the content of information (by means of a figure-of merit) encoded in the amplitude, shape, and full shape of our probes for two-point statistics. The full shape of the luminosity power spectrum, when analyzed up to scales of k~0.2 h/Mpc, yields a figure of merit which is two orders of magnitude above the figure obtained from the unweighted power spectrum, and only one order of magnitude below the value encoded in X-ray luminosity function estimated from the same sample. This is a significant improvement over the analysis developed with the standard (i.e., unweighted) clustering probes. The measurements of the clustering of galaxy clusters and its explicit dependence on the cluster intrinsic properties can contribute to improving the degree of knowledge regarding the underlying links between cluster observables and the cluster masses (Abridged)., Comment: 12 pages, 9 figures. Accepted for publication in Astronomy and Astrophysics

We explore the effects of a positive cosmological constant on astrophysical and cosmological configurations described by a polytropic equation of state. We derive the conditions for equilibrium and stability of such configurations and consider some astrophysical examples where our analysis may be relevant. We show that in the presence of the cosmological constant the isothermal sphere is not a viable astrophysical model since the density in this model does not go asymptotically to zero. The cosmological constant implies that, for polytropic index smaller than five, the central density has to exceed a certain minimal value in terms of the vacuum density in order to guarantee the existence of a finite size object. We examine such configurations together with effects of $\Lambda$ in other exotic possibilities, such as neutrino and boson stars, and we compare our results to N-body simulations. The astrophysical properties and configurations found in this article are specific features resulting from the existence of a dark energy component. Hence, if found in nature would be an independent probe of a cosmological constant, complementary to other observations., Comment: 23 pages, 11 figures, 2 tables. Reference added. Mon. Not. Roy. Astro. Soc in print

We explore local consequences of a non-zero cosmological constant on astrophysical structures. We find that the effects are not only sensitive to the density of the configurations but also to the geometry. For non-homogeneous configurations, we calculate the effects for a polytropic configurations and the isothermal sphere. Special emphasis is put on the fact that the cosmological constant sets certain scales of length, time, mass and density. Sizable effects are established for non spherical systems such as elliptical galaxy clusters where the effects of $\Lambda$ are growing with the flatness of the system. The equilibrium of rotating ellipsoids is modified and the cosmological constant allows new configurations of equilibrium., Comment: talk given at Albert Einstein International Conference in Palais de l'Unesco, Paris, France, 18-23 July 2005; references added

The cosmological constant sets certain scales important in cosmology. We show that Lambda in conjunction with other parameters like the Schwarzschild radius leads to scales relevant not only for cosmological but also for astrophysical applications. Of special interest is the extension of orbits and velocity of test particles traveling over Mpc distances. We will show that there exists a lower and an upper cut-off on the possible velocities of test particles. For a test body moving in a central gravitational field Lambda enforces a maximal value of the angular momentum if we insist on bound orbits of the test body which move at a distance larger than the Schwarzschild radius., Comment: 15 pages, 2 figures, 1 table; one reference added

Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. It is argued that the bound coming from the analysis of exact solutions is not a feature of the relativistic theory since it also emerges from the Newtonian theory. The methods in use seem to be disjoint from the basic principles, however they have the same implication regarding the upper bounds. Therefore we will compare different inequalities and comment on the possible relationship between them., Comment: 19 pages, LaTeX; revised version with new section 8, improved introduction and summary; one reference added