The anisotropy of clustering in redshift space provides a direct measure of the growth rate of large scale structure in the Universe. Future galaxy redshift surveys will make high precision measurements of these distortions, and will potentially allow us to distinguish between different scenarios for the accelerating expansion of the Universe. Accurate predictions are needed in order to distinguish between competing cosmological models. We study the distortions in the redshift space power spectrum in $Λ$CDM and quintessence dark energy models, using large volume N-body simulations, and test predictions for the form of the redshift space distortions. We find that the linear perturbation theory prediction by Kaiser (1987) is a poor fit to the measured distortions, even on surprisingly large scales $k \ge 0.05 h$Mpc$^{-1}$. An improved model for the redshift space power spectrum, including the non-linear velocity divergence power spectrum, is presented and agrees with the power spectra measured from the simulations up to $k \sim 0.2 h$Mpc$^{-1}$. We have found a density-velocity relation which is cosmology independent and which relates the non-linear velocity divergence spectrum to the non-linear matter power spectrum. We provide a formula which generates the non-linear velocity divergence $P(k)$ at any redshift, using only the non-linear matter power spectrum and the linear growth factor at the desired redshift. This formula is accurate to better than 5% on scales $k<0.2 h $Mpc$^{-1}$ for all the cosmological models discussed in this paper. Our results will extend the statistical power of future galaxy surveys.
We investigate the spatial properties of the large scale structure (LSS) of the Universe in the framework of coupled dark energy (cDE) cosmologies. Using the public halo catalogues from the CoDECS simulations -- the largest set of N-body experiments to date for such cosmological scenarios -- we estimate the clustering and bias functions of cold dark matter (CDM) haloes, both in real- and redshift-space. Moreover, we investigate the effects of the dark energy (DE) coupling on the geometric and dynamic redshift-space distortions, quantifying the difference with respect to the concordance LambdaC…
Large-scale structure surveys in the coming years will measure the redshift-space power spectrum to unprecedented accuracy, allowing for powerful new tests of the LambdaCDM picture as well as measurements of particle physics parameters such as the neutrino masses. We extend the Time-RG perturbative framework to redshift space, computing the power spectrum P_s(k,mu) in massive neutrino cosmologies with time-dependent dark energy equations of state w(z). Time-RG is uniquely capable of incorporating scale-dependent growth into the P_s(k,mu) computation, which is important for massive neutrinos as…
Linear Growth of Matter Perturbations Probed by Redshift-Space Distortions in Interacting $Λ(t)$CDM Cosmologies
University of Science and Technology of China（中国科学技术大学）；Universidade Estadual Paulista (UNESP)（圣保罗州立大学）；Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Instituto Nacional de Pesquisas Espaciais（国家空间研究所）；Universidade de São Paulo（圣保罗大学）
We present an updated version of the HMcode augmented halo model that can be used to make accurate predictions of the non-linear matter power spectrum over a wide range of cosmologies. Major improvements include modelling of BAO damping in the power spectrum and an updated treatment of massive neutrinos. We fit our model to simulated power spectra and show that we can match the results with an RMS error of 2.5 per cent across a range of cosmologies, scales $k < 10\,h\mathrm{Mpc}^{-1}$, and redshifts $z<2$. The error rarely exceeds 5 per cent and never exceeds 16 per cent. The worst-case errors…
We show that linear redshift distortions in the galaxy distribution can affect the ISW galaxy-temperature signal, when the galaxy selection function is derived from a redshift survey. We find this effect adds power to the ISW signal at all redshifts and is larger at higher redshifts. Omission of this effect leads to an overestimation of the dark energy density $Ω_Λ$ as well as an underestimation of statistical errors. We find a new expression for the ISW Limber equation which includes redshift distortions, though we find that Limber equations for the ISW calculation are ill-suited for tomograp…
We use Luminous Red Galaxies from the Sloan Digital Sky Survey II to test the cosmological structure growth in two alternatives to the standard LCDM+GR cosmological model. We compare observed three-dimensional clustering in SDSS DR7 with theoretical predictions for the standard vanilla LCDM+GR model, Unified Dark Matter cosmologies and the normal branch DGP. In computing the expected correlations in UDM cosmologies, we derive a parameterized formula for the growth factor in these models. For our analysis we apply the methodology tested in Raccanelli et al. 2010 and use the measurements of Samu…
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…
We develop a model for the redshift-space correlation function, valid for both dark matter particles and halos on scales $>5\,h^{-1}$Mpc. In its simplest formulation, the model requires the knowledge of the first three moments of the line-of-sight pairwise velocity distribution plus two well-defined dimensionless parameters. The model is obtained by extending the Gaussian-Gaussianity prescription for the velocity distribution, developed in a previous paper, to a more general concept allowing for local skewness, which is required to match simulations. We compare the model with the well known Ga…
Interpreting observations of the Lyman-$α$ forest flux power spectrum requires interpolation between a small number of expensive simulations. We present a Gaussian process emulator modelling the 1D flux power spectrum as a function of the amplitude and slope of the small-scale linear matter power spectrum, and the state of the intergalactic medium at the epoch of interest ($2 < z < 4$). This parameterisation enables the prediction of the flux power spectrum in extended cosmological models that are not explicitly included in the training set, eliminating the need to construct bespoke emulators …
Modified gravity and massive neutrino cosmologies are two of the most interesting scenarios that have been recently explored to account for possible observational deviations from the concordance $Λ$-cold dark matter ($Λ$CDM) model. In this context, we investigated the large-scale structure of the Universe by exploiting the \dustp simulations that implement, simultaneously, the effects of $f(R)$ gravity and massive neutrinos. To study the possibility of breaking the degeneracy between these two effects, we analysed the redshift-space distortions in the clustering of dark matter haloes at differ…
As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation $\vec{r}$, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean $μ$ and dispersion $σ$. Based on physical considerations, we make the…
Conditional Diffusion-Flow models for generating 3D cosmic density fields: applications to f(R) cosmologies
Grupo Signos, Departamento de Matemáticas, Universidad El Bosque（埃尔博斯克大学数学系信号组）；Data Science Research Centre, Liverpool John Moores University（利物浦约翰·莫尔斯大学数据科学研究中心）；Departamento de Física, Universidad de Córdoba（科尔多瓦大学物理系）
We construct general anisotropic cosmological scenarios governed by an $f(R)=R^n$ gravitational sector. Focusing then on some specific geometries, and modelling the matter content as a perfect fluid, we perform a phase-space analysis. We analyze the possibility of accelerating expansion at late times, and additionally, we determine conditions for the parameter $n$ for the existence of phantom behavior, contracting solutions as well as of cyclic cosmology. Furthermore, we analyze if the universe evolves towards the future isotropization without relying on a cosmic no-hair theorem. Our results i…
In the context of forthcoming galaxy surveys, to ensure unbiased constraints on cosmology and gravity when using non-linear structure information, percent-level accuracy is required when modelling the power spectrum. This calls for frameworks that can accurately capture the relevant physical effects, while allowing for deviations from $Λ$CDM. Massive neutrino and baryonic physics are two of the most relevant such effects. We present an integration of the halo model reaction frameworks for massive neutrinos and beyond-$Λ$CDM cosmologies. The integrated halo model reaction, combined with a pseud…
Redshift space distortions caused by galaxy peculiar velocities provide a window onto the growth rate of large scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index, γ. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1-sigma or more relative to the fiducial at scales as large as k > 0.07 h/Mpc. This bias propagates to es…
The post-reionization ${\rm HI}$ 21-cm signal is an excellent candidate for precision cosmology, this however requires accurate modelling of the expected signal. Sarkar et al. (2016) have simulated the real space ${\rm HI}$ 21-cm signal, and have modelled the ${\rm HI}$ power spectrum as $P_{\rm HI}(k)=b^2 P(k)$ where $P(k)$ is the dark matter power spectrum and $b(k)$ is a (possibly complex) scale dependent bias for which fitting formulas have been provided. This paper extends these simulations to incorporate redshift space distortion and predict the expected redshift space ${\rm HI}$ 21-cm p…
The combination of two- and three-point clustering statistics of galaxies and the underlying matter distribution has the potential to break degeneracies between cosmological parameters and nuisance parameters and can lead to significantly tighter constraints on parameters describing the composition of the Universe and the dynamics of inflation. Here we investigate the relation between biases in the estimated parameters and inaccurate modelling of non-linear redshift-space distortions for the power spectrum and bispectrum of projected galaxy density fields and lensing convergence. Non-linear re…
Non-linear Structure Formation in Planck+DESI Favoured Interacting Dark Energy Cosmologies
University of Sheffield（谢菲尔德大学）；Durham University（杜伦大学）；Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Instituto Nacional de Pesquisas Espaciais（国家空间研究所）
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 next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys will observe is to use cosmological perturbation theory for linear structures on horizon-sized scales, and Newtonian gravity for non-linear structures on much smaller scales. We propose a two-parameter formalism that generalizes this approach, thereby allowing interactions between large and small scales to be studied in a self-consistent and well-defined way. …
The coming generation of galaxy surveys will provide measurements of galaxy clustering with unprecedented accuracy and data size, which will allow us to test cosmological models at much higher precision than achievable previously. This means that we must have more accurate theoretical predictions to compare with future observational data. As a first step towards more accurate modelling of the redshift space distortions (RSD) of small-scale galaxy clustering in modified gravity (MG) cosmologies, we investigate the validity of the so-called Skew-T (ST) probability distribution function (PDF) of …
Both multi-streaming (random motion) and bulk motion cause the Finger-of-God (FoG) effect in redshift space distortion (RSD). We apply a direct measurement of the multi-streaming effect in RSD from simulations, proving that it induces an additional, non-negligible FoG damping to the redshift space density power spectrum. We show that, including the multi-streaming effect, the RSD modelling is significantly improved. We also provide a theoretical explanation based on halo model for the measured effect, including a fitting formula with one to two free parameters. The improved understanding of Fo…
We implement an adaptation of the COLA approach, a hybrid scheme that combines Lagrangian perturbation theory with an N-body approach, to model non-linear collapse in chameleon and symmetron modified gravity models. Gravitational screening is modeled effectively through the attachment of a suppression factor to the linearized Klein-Gordon equations. The adapted COLA approach is benchmarked, with respect to an N-body code both for the $Λ$CDM scenario and for the modified gravity theories. It is found to perform well in the estimation of the dark matter power spectra, with consistency of 1 % to …
In the expanding Universe, the average temperature of the cosmic microwave background (CMB) is expected to depend like TCMB~(1+z) on redshift z. Adiabatic photon production (or destruction) or deviations from isotropy and homogeneity could modify this scaling and several observational tests have been carried out in response. Here, we explain why `adiabatic' conditions are extremely difficult to establish in the redshift range targeted by these tests. Thus, instead of leading to a simple rescaling of the CMB temperature, a spectral distortion should be produced, which can be constrained using C…
The observed power spectrum in redshift space appears distorted due to the peculiar motion of galaxies, known as redshift-space distortions (RSD). While all the effects in RSD are accounted for by the simple mapping formula from real to redshift spaces, accurately modeling redshift-space power spectrum is rather difficult due to the non-perturbative properties of the mapping. Still, however, a perturbative treatment may be applied to the power spectrum at large-scales, and on top of a careful modeling of the Finger-of-God effect caused by the small-scale random motion, the redshift-space power…
Galaxy surveys aim to map the large-scale structure of the Universe and use redshift space distortions to constrain deviations from general relativity and probe the existence of massive neutrinos. However, the amount of information that can be extracted is limited by the accuracy of theoretical models used to analyze the data. Here, by using the L-Galaxies semi-analytical model run over the MXXL N-body simulation, we assess the impact of galaxy formation on satellite kinematics and the theoretical modelling of redshift-space distortions. We show that different galaxy selection criteria lead to…
The distribution of angles subtended between pairs of galaxies and the line of sight,which is uniform in real space, is distorted by their peculiar motions, and has been proposed as a probe of cosmic expansion. We test this idea using N-body simulations of structure formation in a cold dark matter universe with a cosmological constant and in two variant cosmologies with different dark energy models. We find that the distortion of the distribution of angles is sensitive to the nature of dark energy. However, for the first time, our simulations also reveal dependences of the normalization of the…
We develop a cosmological parameter estimation code for (tomographic) angular power spectra analyses of galaxy number counts, for which we include, for the first time, redshift-space distortions (RSD) in the Limber approximation. This allows for a speed-up in computation time, and we emphasise that only angular scales where the Limber approximation is valid are included in our analysis. Our main result shows that a correct modelling of RSD is crucial not to bias cosmological parameter estimation. This happens not only for spectroscopy-detected galaxies, but even in the case of galaxy surveys w…
Evolution mapping III: A new recipe for the halo mass function
Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理研究所）；Instituto de Astronomía Teórica y Experimental (CONICET-UNC)（理论与实验天文学研究所（阿根廷国家科学研究委员会-科尔多瓦国立大学））；Observatorio Astronómico, Universidad Nacional de Córdoba（科尔多瓦国立大学天文台）；Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München（慕尼黑大学物理学院大学天文台）
We present measurements of the growth rate of cosmological structure from the modelling of the anisotropic galaxy clustering measured in the final data release of the VIPERS survey. The analysis is carried out in configuration space and based on measurements of the first two even multipole moments of the anisotropic galaxy auto-correlation function, in two redshift bins spanning the range $0.5 < z < 1.2$. We provide robust and cosmology-independent corrections for the VIPERS angular selection function, allowing recovery of the underlying clustering amplitude at the percent level down to the Mp…
We present the first cosmological measurement derived from a galaxy density field subject to a `clipping' transformation. By enforcing an upper bound on the galaxy number density field in the Galaxy and Mass Assembly survey (GAMA), contributions from the nonlinear processes of virialisation and galaxy bias are greatly reduced. This leads to a galaxy power spectrum which is easier to model, without calibration from numerical simulations. We develop a theoretical model for the power spectrum of a clipped field in redshift space, which is exact for the case of anisotropic Gaussian fields. Clippin…
The clustering ratio is defined as the ratio between the correlation function and the variance of the smoothed overdensity field. In LCDM cosmologies not accounting for massive neutrinos, it has already been proved to be independent from bias and redshift space distortions on a range of linear scales. It therefore allows for a direct comparison of measurements (from galaxies in redshift space) to predictions (for matter in real space). In this paper we first extend the applicability of such properties of the clustering ratio to cosmologies that include massive neutrinos, by performing tests ag…
Redshift space distortions (RSD) in the void-galaxy correlation $ξ^s$ provide information on the linear growth rate of structure in low density environments. Accurate modelling of these RSD effects can also allow the use of voids in competitive Alcock-Paczynski measurements. Linear theory models of $ξ^s$ are able to provide extremely good descriptions of simulation data on all scales provided the real space void positions are known. However, by reference to simulation data we demonstrate the failure of the assumptions implicit in current models of $ξ^s$ for voids identified directly in redshif…
The velocity divergence power spectrum is a key ingredient in modelling redshift space distortion effects on quasi-linear and nonlinear scales. We present an improved model for the z=0 velocity divergence auto and cross power spectrum which was originally suggested by Jennings et al. 2011. Using numerical simulations we measure the velocity fields using a Delaunay tesselation and obtain an accurate prediction of the velocity divergence power spectrum on scales k < 1 hMpc^{-1}. We use this to update the model which is now accurate to 2% for both P_{θθ} and P_{θδ} at z=0 on scales k <0.7 hMpc^{-…
We present a Bayesian reconstruction method which maps a galaxy distribution from redshift-space to real-space inferring the distances of the individual galaxies. The method is based on sampling density fields assuming a lognormal prior with a likelihood given by the negative binomial distribution function modelling stochastic bias. We assume a deterministic bias given by a power law relating the dark matter density field to the expected halo or galaxy field. Coherent redshift-space distortions are corrected in a Gibbs-sampling procedure by moving the galaxies from redshift-space to real-space…
We present the first simultaneous analysis of the galaxy overdensity and peculiar velocity fields by modelling their cross-covariance. We apply our new maximum-likelihood approach to data from the 6-degree Field Galaxy Survey (6dFGS), which has the largest single collection of peculiar velocities to date. We present a full derivation of the analytic expression for the cross-covariance between the galaxy overdensity and peculiar velocity fields and find direct evidence for a non-zero correlation between the fields on scales up to $\sim50 h^{-1}$ Mpc. When utilising the cross-covariance, our mea…
We use large volume N-body simulations to predict the clustering of dark matter in redshift space in f(R) modified gravity cosmologies. This is the first time that the nonlinear matter and velocity fields have been resolved to such a high level of accuracy over a broad range of scales in this class of models. We find significant deviations from the clustering signal in standard gravity, with an enhanced boost in power on large scales and stronger damping on small scales in the f(R) models compared to GR at redshifts z<1. We measure the velocity divergence (P_θθ) and matter (P_δδ) power spectra…
Using cosmic voids to probe the growth rate of cosmic structure, and hence the nature of dark energy, is particularly interesting in the context of modified gravity theories that rely on the screening mechanism. In this work we improve the modelling of redshift-space distortions around voids in the dark matter density field, and thus reduce systematic errors in the derivation of cosmological parameters. We also show how specific types of voids can be used to better probe the growth rate, using a flexible void finder. We apply our results to test for a quintessence type of dark energy vs. a LCD…
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…
Biased tracers, Hybrid Effective Field Theory and Modified Gravity
CBPF - Brazilian Center for Research in Physics（巴西物理研究中心）；Institute for Computational Cosmology, Department of Physics, Durham University（杜伦大学）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学）
In the standard (classic) approach, galaxy clustering measurements from spectroscopic surveys are compressed into baryon acoustic oscillations and redshift space distortions measurements, which in turn can be compared to cosmological models. Recent works have shown that avoiding this intermediate step and fitting directly the full power spectrum signal (full modelling) leads to much tighter constraints on cosmological parameters. Here we show where this extra information is coming from and extend the classic approach with one additional effective parameter, such that it captures, effectively, …
Weak lensing (WL) clustering is studied using 2D (angular) coordinates, while redshift space distortions (RSD) and baryon acoustic oscillations (BAO) use 3D coordinates, which requires a model dependent conversion of angles and redshifts into comoving distances. This is the first paper of a series, which explore modelling multi-tracer galaxy clustering (of WL, BAO and RSD), using only angular (2D) cross-correlations in thin redshift bins. This involves evaluating many thousands cross-correlations, each a multidimensional integral, which is computationally demanding. We present a new algorithm …
We present improved modelling of the redshift-space distortions of galaxy clustering that arise from peculiar velocities. We create mock galaxy catalogues in the framework of the halo model, using data from the Bolshoi project. These mock galaxy populations are inserted into the haloes with additional degrees of freedom that govern spatial and kinematical biases of the galaxy populations relative to the dark matter. We explore this generalised halo model with an MCMC algorithm, comparing the predictions to data from the Galaxy And Mass Assembly (GAMA) survey, and thus derive one of the first c…
The {\rm HI} 21-cm intensity mapping signal experiences redshift space distortions due to the motion of the galaxies which contain the {\rm HI} as well as the motions of the {\rm HI} gas within the galaxies. A detailed modelling is essential if this signal is to be used for precision cosmology. Considering dark matter only simulations where the {\rm HI} is assumed to reside in galaxies which are associated with haloes, in this work we introduce a technique to incorporate the {\rm HI} motions within the galaxies. This is achieved through a line profile which accounts for both the rotational and…
The tomographic Alcock-Paczynski (AP) method utilizes the redshift evolution of the AP distortion to place constraints on cosmological parameters. It has proved to be a robust method that can separate the AP signature from the redshift space distortion (RSD) effect, and deliver powerful cosmological constraints using the $\lesssim 40h^{-1}\ \rm Mpc$ clustering region. In previous works, the tomographic AP method was performed via the anisotropic 2-point correlation function statistic. In this work we consider the feasibility of conducting the analysis in the Fourier domain and examine the pros…
We derive the expression for the observed redshift in the weak field limit in the observer's past light cone, including all relativistic terms up to second order in velocity. We then apply it to compute the cluster-galaxy cross-correlation functions (CGCF) using N-body simulations. The CGCF is asymmetric along the line of sight (LOS) owing to the presence of the small second order terms such as the gravitational redshift (GRedshift). We identify two systematics in the modelling of the GRedshift signal in stacked clusters. First, it is affected by the morphology of dark matter haloes and the la…
Small- and intermediate-scale galaxy clustering can be used to establish the galaxy-halo connection to study galaxy formation and evolution and to tighten constraints on cosmological parameters. With the increasing precision of galaxy clustering measurements from ongoing and forthcoming large galaxy surveys, accurate models are required to interpret the data and extract relevant information. We introduce a method based on high-resolution N-body simulations to accurately and efficiently model the galaxy two-point correlation functions (2PCFs) in projected and redshift spaces. The basic idea is …
Accurate modelling of redshift-space distortions (RSD) is challenging in the non-linear regime for two-point statistics e.g. the two-point correlation function (2PCF). We take a different perspective to split the galaxy density field according to the local density, and cross-correlate those densities with the entire galaxy field. Using mock galaxies, we demonstrate that combining a series of cross-correlation functions (CCFs) offers improvements over the 2PCF as follows: 1. The distribution of peculiar velocities in each split density is nearly Gaussian. This allows the Gaussian streaming mode…
Improving the theoretical description of galaxy clustering on small scales is an important challenge in cosmology, as it can considerably increase the scientific return of forthcoming galaxy surveys -- e.g. tightening the bounds on neutrino masses and deviations from general relativity. In this paper, we propose and test a new model for the clustering of galaxies that is able to accurately describe redshift-space distortions even down to small scales. This model corresponds to a second-order perturbative Lagrangian bias expansion which is advected to Eulerian space employing a displacement fie…
To understand the nature of the accelerated expansion of the Universe, we need to combine constraints on the expansion rate and growth of structure. The growth rate is usually extracted from three dimensional galaxy maps by exploiting the effects of peculiar motions on galaxy clustering. However, theoretical models of the probability distribution function (PDF) of galaxy pairwise peculiar velocities are not accurate enough on small scales to reduce the error on theoretical predictions to the level required to match the precision expected for measurements from future surveys. Here, we improve t…
