Since the volume accessible to galaxy surveys is fundamentally limited, it is extremely important to analyse available data in the most optimal fashion. One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region (FKP weights) and their bias with respect to the dark matter field (PVP weights). They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. We develop a procedure for computing the optimal weights and test them against mock catalogues for which the values of all fitting parameters, as well as the input power-spectrum are known. We show that by applying these weights to the joint power-spectrum of Emission Line Galaxies and Luminous Red Galaxies from the Dark Energy Spectroscopic Instrument survey, the variance in the measured growth rate parameter can be reduced by as much as 36 per cent.
We produce 1000 realizations of synthetic clustering catalogues for each type of the tracers used for the baryon acoustic oscillation and redshift space distortion analysis of the Sloan Digital Sky Surveys-IV extended Baryon Oscillation Spectroscopic Survey final data release (eBOSS DR16), covering the redshift range from 0.6 to 2.2, to provide reliable estimates of covariance matrices and test the robustness of the analysis pipeline with respect to observational systematics. By extending the Zel'dovich approximation density field with an effective tracer bias model calibrated with the cluster…
We show how to obtain constraints on $β=f/b$, the ratio of the matter growth rate and the bias that quantifies the linear redshift-space distortions, that are independent of the cosmological model, using multiple tracers of large-scale structure. For a single tracer the uncertainties on $β$ are constrained by the uncertainties in the amplitude and shape of the power spectrum, which is limited by cosmic variance. However, for two or more tracers this limit does not apply, since taking the ratio of power spectra cosmic variance cancels out, and in the linear (Kaiser) approximation one measures d…
We investigate clustering properties of dark matter halos and galaxies to search for optimal statistics and scales where possible departures from general relativity (GR) could be found. We use large N-body cosmological simulations to perform measurements based on the two-point correlation function (2PCF) in GR and in selected modified gravity (MG) structure formation scenarios. As a test-bed, we employ two popular beyond-GR models: $f(R)$ gravity and the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld. We study a range of simulated halo and galaxy populations and reveal a notice…
Accurate mock catalogues are essential for assessing systematics in the cosmological analysis of large galaxy surveys. Anisotropic two-point clustering measurements from the same simulation show some scatter for different lines of sight (LOS), but are on average equal, due to cosmic variance. This results in scatter in the measured cosmological parameters. We use the OuterRim N-body simulation halo catalogue to investigate this, considering the 3 simulation axes as LOS. The quadrupole of the 2-point statistics is particularly sensitive to changes in the LOS, with sub-percent level differences …
We measure Redshift-Space Distortions (RSD) in the two-point correlation function of a sample of $63,163$ spectroscopically identified galaxies with $z < 0.2$, an epoch where there are currently only limited measurements, from the Sloan Digital Sky Survey (SDSS) Data Release 7 Main Galaxy Sample. Our sample, which we denote MGS, covers 6,813 deg$^2$ with an effective redshift $z_{eff}=0.15$ and is described in our companion paper (Paper I), which concentrates on BAO measurements. In order to validate the fitting methods used in both papers, and derive errors, we create and analyse 1000 mock ca…
Peculiar-velocity surveys of the low-redshift universe have significant leverage to constrain the growth rate of cosmic structure and test gravity. Wide-field imaging surveys combined with multi-object spectrographs (e.g. ZTF2, LSST, DESI, 4MOST) can use Type Ia supernovae as informative tracers of the velocity field, reaching few percent constraints on the growth rate $fσ_8$ at $z\lesssim0.2$ where density tracers cannot do better than $\sim10\%$. Combining the high-redshift DESI survey mapping redshift space distortions with a low-redshift supernova peculiar velocity survey using LSST and DE…
The information extracted from large galaxy surveys with the likes of DES, DESI, Euclid, LSST, SKA, and WFIRST will be greatly enhanced if the resultant galaxy catalogues can be cross-correlated with one another. Predicting the nature of the information gain, and developing the tools to realise it, depends on establishing a consistent model of how the galaxies detected by each survey trace the same underlying matter distribution. Existing analytic methods, such as halo occupation distribution (HOD) modelling, are not well-suited for this task, and can suffer from ambiguities and tuning issues …
Using multiple tracers of large-scale structure allows to evade the limitations imposed by sampling variance for some parameters of interest in cosmology. We demonstrate the optimal way of carrying out a multitracer analysis in a galaxy redshift survey by considering the principal components of the shot noise matrix from two-point clustering statistics. We show how to construct two tracers that maximize the benefits of sampling variance and shot noise cancellation using optimal weights. On the basis of high-resolution N-body simulations of dark matter halos we apply this technique to the analy…
The gravitational coupling between large- and small-scale density perturbations leads to anisotropic distortions to the local small-scale matter fluctuations. Such local anisotropic distortions can be used to reconstruct the large-scale matter distribution, known as tidal reconstruction. In this paper, we apply the tidal reconstruction methods to simulated galaxies in redshift space. We find that redshift-space distortions lead to anisotropic reconstruction results. While the reconstructed radial modes are more noisy mainly due to the small-scale velocity dispersion, the transverse modes are s…
Galaxy filaments are the dominant feature in the overall structure of the cosmic web. The study of the filamentary web is an important aspect in understanding galaxy evolution and the evolution of matter in the Universe. A map of the filamentary structure is an adequate probe of the web. We propose that photometric redshift galaxies are significantly positively associated with the filamentary structure detected from the spatial distribution of spectroscopic redshift galaxies. The catalogues of spectroscopic and photometric galaxies are seen as point-process realisations in a sphere, and the ca…
We construct cosmic void catalogues with the DIVE void finder upon SDSS BOSS DR12 and eBOSS DR16 galaxy samples with BAO reconstruction applied, and perform a joint BAO analysis using different types of galaxies and the corresponding voids. The BAO peak is evident for the galaxy-galaxy, galaxy-void, and void-void correlation functions of all datasets, including the ones cross correlating luminous red galaxy and emission line galaxy samples. Two multi-tracer BAO fitting schemes are then tested, one combining the galaxy and void correlation functions with a weight applied to voids, and the other…
General and explicit predictions from the integrated perturbation theory (iPT) for power spectra and correlation functions of biased tracers are derived and presented in the one-loop approximation. The iPT is a general framework of the nonlinear perturbation theory of cosmological density fields in presence of nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. Analytic formulas of auto and cross power spectra of nonlocally biased tracers in both real and redshift spaces are derived and the results are comprehensively summarized. The main difference from previous formula…
We investigate the performance of group finding algorithms that reconstruct galaxy groups from the positional information of tracer galaxies that are observed in redshift surveys carried out with multiplexed spectrographs. We use mock light-cones produced by the L-Galaxies semi-analytic model of galaxy evolution in which the underlying reality is known. We particularly focus on the performance at high redshift, and how this is affected by choices of the mass of the tracer galaxies (largely equivalent to their co-moving number density) and the (assumed random) sampling rate of these tracers. We…
Using the redshift-space distortions of void-galaxy cross-correlation function we analyse the dynamics of voids embedded in different environments. We compute the void-galaxy cross-correlation function in the Sloan Digital Sky Survey (SDSS) in terms of distances taken along the line of sight and projected into the sky. We analyse the distortions on the cross-correlation isodensity levels and we find anisotropic isocontours consistent with expansion for large voids with smoothly rising density profiles and collapse for small voids with overdense shells surrounding them. Based on the linear appr…
Galaxy surveys that map multiple species of tracers of large-scale structure can improve the constraints on some cosmological parameters far beyond the limits imposed by a simplistic interpretation of cosmic variance. This enhancement derives from comparing the relative clustering between different tracers of large-scale structure. We present a simple but fully generic expression for the Fisher information matrix of surveys with any (discrete) number of tracers, and show that the enhancement of the constraints on bias-sensitive parameters are a straightforward consequence of this multi-tracer …
We present the first application of a "multiple-tracer" redshift-space distortion (RSD) analysis to an observational galaxy sample, using data from the Galaxy and Mass Assembly survey (GAMA). Our dataset is an r < 19.8 magnitude-limited sample of 178,579 galaxies covering redshift interval z < 0.5 and area 180 deg^2. We obtain improvements of 10-20% in measurements of the gravitational growth rate compared to a single-tracer analysis, deriving from the correlated sample variance imprinted in the distributions of the overlapping galaxy populations. We present new expressions for the covariances…
We develop a new Multi-Tracer Halo Occupation Distribution (\texttt{MTHOD}) framework for the galaxy distribution and apply it to the extended Baryon Oscillation Spectroscopic Survey (eBOSS) final data between $z=0.7-1.1$. We obtain a best fit \mthod\, for each tracer and describe the host halo properties of these galaxies. The mean halo masses for LRGs, ELGs and QSOs are found to be $1.9 \times 10^{13} \msolaroh$, $1.1 \times 10^{12} \msolaroh$ and $5 \times 10^{12} \msolaroh$ respectively in the eBOSS data. We use the \texttt{MTHOD} framework to create mock galaxy catalogues and predict auto…
We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feldman, Kaiser & Peacock (ApJ 1994, FKP) in the case of a survey consisting of a single species of tracer.…
The redshift-space distortion (RSD) of galaxies surrounding massive clusters is emerging as a promising testbed for theories of modified gravity. Conventional applications of this method rely upon the assumption that the velocity field in the cluster environment is uniquely determined by the cluster mass profile. Yet, real dark matter halos in N-body simulations are known to violate the assumption that virial mass determines the configuration space distribution, an effect known as assembly bias. In this Letter, I show that assembly bias in simulated dark matter halos also manifests in velocity…
The velocity profile of galaxies around voids is a key ingredient for redshift space distortion (RSD) measurements made using the void-galaxy correlation function. In this paper we use simulations to test whether the velocity profile of the tracers used to find the voids matches the velocity profile of the dark matter around these voids. A mismatch is expected and found in the inner part of voids, where tracers are very sparse. We discuss how this difference is caused by a selection effect where the void centre positions are correlated to the particular realization of the sparse tracers and th…
The Baryon Acoustic Oscillations (BAO) refer to the ripples of material density in the Universe. As the most direct density tracers in the universe, galaxies have been commonly used in studies of BAO peak detection. The spatial number density of galaxies, to a certain extent, reflects the distribution of the material density of our Universe. Using galaxies as matter tracers, we can construct more overlapping empty spheres (DT voids) than the matter tracers, via Delaunay Triangulation technique. We show that their radii excellently reflect the galaxy number density round them, and they can serv…
Clustering measurements of Gravitational Wave (GW) mergers in Luminosity Distance Space can be used in the future as a powerful tool for Cosmology. We consider tomographic measurements of the Angular Power Spectrum of mergers both in an Einstein Telescope-like detector network and in some more advanced scenarios (more sources, better distance measurements, better sky localization). We produce Fisher forecasts for both cosmological (matter and dark energy) and merger bias parameters. Our fiducial model for the number distribution and bias of GW events is based on results from hydrodynamical sim…
We use the Fisher matrix formalism to study the expansion and growth history of the Universe using galaxy clustering with 2D angular cross-correlation tomography in spectroscopic or high resolution photometric redshift surveys. The radial information is contained in the cross correlations between narrow redshift bins. We show how multiple tracers with redshift space distortions cancel sample variance and arbitrarily improve the constraints on the dark energy equation of state $ω(z)$ and the growth parameter $γ$ in the noiseless limit. The improvement for multiple tracers quickly increases with…
In this paper, we apply the multi-tracer technique to harmonic-space (i.e.\ angular) power spectra with a likelihood-based approach. This goes beyond the usual Fisher matrix formalism hitherto implemented in forecasts with angular statistics, opening up a window for future developments and direct application to available data sets. We also release a fully-operational modified version of the publicly available code CosmoSIS, where we consistently include all the add-ons presented in the previous papers of this series. The result is a modular cosmological parameter estimation suite for angular p…
The study of the cross-correlation angular power spectrum between gravitational tracers and electromagnetic signals can be a powerful tool to constrain Dark Matter (DM) microscopic properties. In this work we correlate \Fermi\ diffuse \g-ray maps with catalogues of galaxy clusters. To emphasize the sensitivity to a DM signal, we select clusters at low-redshift $0<z<0.2$ and with large-halo mass $M_{500}>10^{13}M_\odot$. The analysis is performed with four catalogues in different wavebands, including infrared, optical and X-rays. No evidence for a DM signal is identified. On the other hand, we …
Measurements of redshift space distortions (RSD) provide a means to test models of gravity on large-scales. We use mock galaxy catalogues constructed from large N-body simulations of standard and modified gravity models to measure galaxy clustering in redshift space. We focus our attention on two of the most representative and popular families of modified gravity models: the Hu \& Sawicki $f(R)$ gravity and the normal branch of the DGP model. The galaxy catalogues are built using a halo occupation distribution (HOD) prescription with the HOD parameters in the modified gravity models tuned to m…
We investigate the ability of state-of-the-art redshift-space distortions models for the galaxy anisotropic two-point correlation function ξ(r_p, π), to recover precise and unbiased estimates of the linear growth rate of structure f, when applied to catalogues of galaxies characterised by a realistic bias relation. To this aim, we make use of a set of simulated catalogues at z = 0.1 and z = 1 with different luminosity thresholds, obtained by populating dark-matter haloes from a large N-body simulation using halo occupation prescriptions. We examine the most recent developments in redshift-spac…
Future galaxy surveys require realistic mock catalogues to understand and quantify systematics in order to make precise cosmological measurements. We present a halo lightcone catalogue and halo occupation distribution (HOD) galaxy catalogue built using the Millennium-XXL (MXXL) simulation. The halo catalogue covers the full sky, extending to z = 2 with a mass resolution of ~1e11 Msun/h . We use this to build a galaxy catalogue, which has an r-band magnitude limit of r < 20.0, with a median redshift of z~0.2. A Monte Carlo HOD method is used to assign galaxies to the halo lightcone catalogue, a…
We discover analytic equations that can infer the value of $Ω_{\rm m}$ from the positions and velocity moduli of halo and galaxy catalogues. The equations are derived by combining a tailored graph neural network (GNN) architecture with symbolic regression. We first train the GNN on dark matter halos from Gadget N-body simulations to perform field-level likelihood-free inference, and show that our model can infer $Ω_{\rm m}$ with $\sim6\%$ accuracy from halo catalogues of thousands of N-body simulations run with six different codes: Abacus, CUBEP$^3$M, Gadget, Enzo, PKDGrav3, and Ramses. By app…
We investigate the impact of statistical and systematic errors on measurements of linear redshift-space distortions (RSD) in future cosmological surveys, analyzing large catalogues of dark-matter halos from the BASICC simulation. These allow us to estimate the dependence of errors on typical survey properties, as volume, galaxy density and mass (i.e. bias factor) of the adopted tracer. We find that measures of the specific growth rate β=f/b using the Hamilton/Kaiser harmonic expansion of the redshift-space correlation function ξ(r_p,π) on scales larger than 3/h Mpc are typically under-estimate…
Galaxies and clusters embedded in the large-scale structure of the Universe are observed to align in preferential directions. Galaxy alignment has been established as a potential probe for cosmological information, but the application of cluster alignments for these purposes remains unexplored. Clusters are observed to have a higher alignment amplitude than galaxies, but because galaxies are much more numerous, the trade-off in detectability between the two signals remains unclear. We present forecasts comparing cluster and galaxy alignments for two extragalactic survey set-ups: a currently-av…
The combination of Galaxy-Galaxy Lensing (GGL) and Redshift Space Distortion of galaxy clustering (RSD) is a privileged technique to test General Relativity predictions, and break degeneracies between the growth rate of structure parameter $f$ and the amplitude of the linear power-spectrum $σ_8$. We perform a joint GGL and RSD analysis on 250 sq. degrees using shape catalogues from CFHTLenS and CFHT-Stripe 82, and spectroscopic redshifts from the BOSS CMASS sample. We adjust a model that includes non-linear biasing, RSD and Alcock-Paczynski effects. We find $f(z=0.57) =0.95\pm0.23$, $σ_8(z=0.5…
Redshift-space distortions are generally considered in the plane parallel limit, where the angular separation between the two sources can be neglected. Given that galaxy catalogues now cover large fractions of the sky, it becomes necessary to consider them in a formalism which takes into account the wide angle separations. In this article we derive an operational formula for the matter correlators in the Newtonian limit to be used in actual data sets, both in configuration and in Fourier spaces without relying on a plane-parallel approximation. We then recover the plane-parallel limit not only…
Percolation analysis has long been used to quantify the connectivity of the cosmic web. Most of the previous work is based on density fields on grids. By smoothing into fields, we lose information about galaxy properties like shape or luminosity. Lack of mathematical model also limits our understanding of percolation analysis. In order to overcome these difficulties, we have studied percolation analysis based on discrete points. Using a Friends-of-Friends (FoF) algorithm, we generate the S-bb relation, between the fractional mass of the largest connected group (S) and the FoF linking length (b…
We utilise mock catalogues from high-accuracy cosmological $N$-body simulations to quantify shifts in the recovery of the acoustic scale that could potentially result from galaxy clustering bias. The relationship between galaxies and dark matter halos presents a complicated source of systematic errors in modern redshift surveys, particularly when aiming to make cosmological measurements to sub-percent precision. Apart from a scalar, linear bias parameter accounting for the density contrast ratio between matter tracers and the true matter distribution, other types of galaxy bias, such as assemb…
We present a new model for the cross-covariance between galaxy redshift-space distortions and peculiar velocities. We combine this with the auto-covariance models of both probes in a fully self-consistent, maximum-likelihood method, allowing us to extract enhanced cosmological parameter constraints. When applying our method to the 6-degree Field Galaxy Survey (6dFGS), our constraint on the growth rate of structure is $fσ_8 = 0.384 \pm 0.052 \rm{(stat)} \pm 0.061 \rm{(sys)}$ and our constraint for the redshift-space distortion parameter is $β= 0.289^{+0.044}_{-0.043} \rm{(stat)} \pm 0.049 \rm{(…
The correlation between the large-scale distribution of galaxies and their spectroscopic properties at z=1.5 is investigated using the Horizon MareNostrum cosmological run. We have extracted a large sample of 10^5 galaxies from this large hydrodynamical simulation featuring standard galaxy formation physics. Spectral synthesis is applied to these single stellar populations to generate spectra and colours for all galaxies. We use the skeleton as a tracer of the cosmic web and study how our galaxy catalogue depends on the distance to the skeleton. We show that galaxies closer to the skeleton ten…
Redshift-space clustering anisotropies caused by cosmic peculiar velocities provide a powerful probe to test the gravity theory on large scales. However, to extract unbiased physical constraints, the clustering pattern has to be modelled accurately, taking into account the effects of non-linear dynamics at small scales, and properly describing the link between the selected cosmic tracers and the underlying dark matter field. We use a large hydrodynamic simulation to investigate how the systematic error on the linear growth rate, $f$, caused by model uncertainties, depends on sample selections …
The large-scale redshift-space distortion (RSD) in galaxy clustering can probe $fσ_8$, a combination of the cosmic structure growth rate and the matter fluctuation amplitude, which can constrain dark energy models and test theories of gravity. While the RSD on small scales (e.g. a few to tens of $h^{-1}{\rm Mpc}$) can further tighten the $fσ_8$ constraints, galaxy assembly bias, if not correctly modelled, may introduce systematic uncertainties. Using a mock galaxy catalogue with built-in assembly bias, we perform a preliminary study on how assembly bias may affect the $fσ_8$ inference. We find…
We study the impact on the galaxy correlation function of the presence of a vector component in the tracers' peculiar velocities, in the case in which statistical isotropy is violated. We present a general framework - based on the bipolar spherical harmonics expansion - to study this effect in a model independent way, without any hypothesis on the origin or the properties of these vector modes. We construct six new observables, that can be directly measured in galaxy catalogs in addition to the standard monopole, quadrupole and hexadecapole, and we show that they completely describe any deviat…
We measure the large-scale intrinsic alignments of galaxy clusters in the Sloan Digital Sky Survey (SDSS) using subsets of two cluster catalogues: 6625 clusters with 0.1<z<0.3 from the maxBCG cluster catalogue (Koester et al. 2007, 7500 sq. deg.), and 8081 clusters with 0.08<z<0.44 from the Adaptive Matched Filter catalogue (Dong et al. 2008, 6500 sq. deg.). We search for two types of cluster alignments using pairs of clusters: the alignment between the projected major axes of the clusters (`correlation' alignment), and the alignment between one cluster major axis and the line connecting it to…
We incorporate the effects of redshift space distortions and non-linear bias in time-sliced perturbation theory (TSPT). This is done via a new method that allows to map cosmological correlation functions from real to redshift space. This mapping preserves a transparent infrared (IR) structure of the theory and provides us with an efficient tool to study non-linear infrared effects altering the pattern of baryon acoustic oscillations (BAO) in redshift space. We give an accurate description of the BAO by means of a systematic resummation of Feynman diagrams guided by well-defined power counting …
We present an independent cosmic shear analysis of the non-cosmological B-mode distortions within the public first year data from the Dark Energy Survey (DES). We find no significant detection of B-modes in a full tomographic analysis of the primary METACALIBRATION shear catalogue. This is in contrast to the secondary IM3SHAPE shear catalogue, where we detect B- modes at a significance of $\sim 3σ$ with a pattern that is consistent with the B-mode signature of a repeating additive shear bias across the survey. We use the COSEBIs statistic to cleanly separate the B-modes from the gravitational …
Understanding the formation and evolution of large-scale structure is a central problem in cosmology and enables precise tests of General Relativity on cosmological scales and constraints on dark energy. An essential ingredient is an accurate description of the pairwise velocities of biased tracers of the matter field. In this paper we compute the first and second moments of the pairwise velocity distribution by extending the Convolution Lagrangian Perturbation theory (CLPT) formalism of Carlson et al. (2012). Our predictions outperform standard perturbation theory calculations in many cases w…
We investigate the future perspectives of the detection of the relativistic dipole by cross-correlating the 21 cm emission in Intensity Mapping (IM) and galaxy surveys at low redshift. We model the neutral hydrogen (HI) and the galaxy population by means of the halo model to relate the parameters that affect the dipole signal such as the biases of the two tracers and the Poissonian noise. We investigate the behavior of the signal-to-noise as a function of the galaxy and magnification biases, for two fixed models of the neutral hydrogen. In both cases we found that the signal-to-noise does not …
Observations of galaxy clustering are made in redshift space, which results in distortions to the underlying isotropic distribution of galaxies. These redshift-space distortions (RSD) not only degrade important features of the matter density field, such as the baryonic acoustic oscillation (BAO) peaks, but also pose challenges for the theoretical modelling of observational probes. Here we introduce an iterative nonlinear reconstruction algorithm to remove RSD effects from galaxy clustering measurements, and assess its performance by using mock galaxy catalogues. The new method is found to be a…
The weak gravitational lensing distortion of distant galaxy images (defined as sources) probes the projected large-scale matter distribution in the Universe. To improve quality in the 3D mass mapping using 3D-lensing, we combine the lensing information with the spatial clustering of a population of galaxies that trace the matter density with a known galaxy bias (defined as tracers). For our minimum variance estimator, merely all the second-order bias of the tracers has to be known, which can in principle be self-consistently constrained in the data by lensing techniques. This synergy introduce…
The massive exploitation of cosmic voids for precision cosmology in the upcoming dark energy experiments, requires a robust understanding of their internal structure, particularly of their density profile. We show that the void density profile is insensitive to the void radius both in a catalogue of observed voids and in voids from a large cosmological simulation. However, the observed and simulated voids display remarkably different profile shapes, with the former having much steeper profiles than the latter. Sparsity can not be the main reason for this discrepancy, as we demonstrate that the…
We present a comparison of major methodologies of fast generating mock halo or galaxy catalogues. The comparison is done for two-point and the three-point clustering statistics. The reference catalogues are drawn from the BigMultiDark N-body simulation. Both friend-of-friends (including distinct halos only) and spherical overdensity (including distinct halos and subhalos) catalogs 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 quasilinear and even smaller scales. With…
Luminous tracers of large-scale structure are not entirely representative of the distribution of mass in our Universe. As they arise from the highest peaks in the matter density field, the spatial distribution of luminous objects is biased towards those peaks. On large scales, where density fluctuations are mild, this bias simply amounts to a constant offset in the clustering amplitude of the tracer, known as linear bias. In this work we focus on the relative bias between galaxies and galaxy clusters that are located inside and in the vicinity of cosmic voids, extended regions of relatively lo…
The peculiar velocities of biased tracers of the cosmic density field contain important information about the growth of large scale structure and generate anisotropy in the observed clustering of galaxies. Using N-body data, we show that velocity expansions for halo redshift-space power spectra are converged at the percent-level at perturbative scales for most line-of-sight angles $μ$ when the first three pairwise velocity moments are included, and that the third moment is well-approximated by a counterterm-like contribution. We compute these pairwise-velocity statistics in Fourier space using…
The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result fo…
