We present a Bayesian hierarchical framework for a principled data analysis pipeline of peculiar velocity surveys, which makes explicit the inference problem of constraining cosmological parameters from redshift-independent distance indicators. We demonstrate our method for a Fundamental Plane-based survey. The essence of our approach is to work closely with observables (e.g. angular size, surface brightness, redshift, etc), through which we bypass the use of summary statistics by working with the probability distributions. The hierarchical approach improves upon the usual analysis in several ways. In particular, it allows a consistent analysis without having to make prior assumptions about cosmology during the calibration phase. Moreover, calibration uncertainties are correctly accounted for in parameter estimation. Results are presented for a new, fully analytic posterior marginalised over all latent variables, which we expect to allow for more principled analyses in upcoming surveys. A maximum a posteriori estimator is also given for peculiar velocities derived from Fundamental Plane data.
The line-of-sight peculiar velocities are good indicators of the gravitational fluctuation of the density field. Techniques have been developed to extract cosmological information from the peculiar velocities in order to test the cosmological models. These techniques include measuring cosmic flow, measuring two-point correlation and power spectrum of the peculiar velocity fields, reconstructing the density field using peculiar velocities. However, some measurements from these techniques are biased due to the non-Gaussianity of the estimated peculiar velocities. Therefore, we use the 2MTF surve…
We present a list of distances and peculiar velocities for 1623 RFGC galaxies for three models of collective large-scale galaxy motion on distances about $100 h^{-1}$ Mpc. It is based upon the article [arXiv:0910.4640]. The ASCII version of the list can be downloaded from the AO KNU website: http://www.observ.univ.kiev.ua/data/rfgcvpec.zip
The way that peculiar velocities are often inferred from measurements of distances and redshifts makes an approximation, v_p = cz-H_0 D, that gives significant errors even at relatively low redshifts (overestimates peculiar velocity by ~ 100 km/s at z~0.04). Here we demonstrate where the approximation breaks down, the systematic offset it introduces, and how the exact calculation should be implemented.
How do peculiar velocities affect observed voids? To answer this question we use the VIDE toolkit to identify voids in mock galaxy populations embedded within an N-body simulation both with and without peculiar velocities included. We compare the resulting void populations to assess the impact on void properties. We find that void abundances and spherically-averaged radial density profiles are mildly affected by peculiar velocities. However, peculiar velocities can distort by up to 10% the shapes for a particular subset of voids depending on the void size and density contrast, which can lead t…
Peculiar velocities are an important probe of the growth rate of mass density fluctuations in the Universe. Most previous studies have focussed exclusively on measuring peculiar velocities at intermediate ($0.2 < z < 1$) redshifts using statistical redshift-space distortions. Here we emphasize the power of peculiar velocities obtained directly from distance measurements at low redshift ($z \lesssim 0.05$), and show that these data break the usual degeneracies in the Ω_{m,0} -- $σ_{8,0}$ parameter space. Using only peculiar velocity data, we find $Ω_{m,0} = 0.259\pm0.045$ and $σ_{8,0} = 0.748\p…
The most intriguing question of modern astronomy is the question of our Universe formation. The Hubble diagram analysis with Type Ia Supernovae (SNe Ia) is widely used to estimate the cosmological parameters with high accuracy. The cosmological measurements allow us to better understand the early stages of the Universe evolution. Nevertheless, the redshift on the SN Ia Hubble diagram includes the contribution from the unknown peculiar velocities that decreases the accuracy of such measurements. We consider the contamination of peculiar velocities of the host galaxies for those SNe that explode…
Peculiar velocities, obtained from direct distance measurements, are data of choice to achieve constrained simulations of the Local Universe reliable down to a scale of a few Megaparsecs. Unlike redshift surveys, peculiar velocities are direct tracers of the underlying gravitational field as they trace both baryonic and dark matter. This paper presents the first attempt to use solely observational peculiar velocities to constrain cosmological simulations of the nearby universe. In order to set up Initial Conditions, a Reverse Zel'dovich Approximation (RZA) is used to displace constraints from …
Peculiar velocities of type Ia supernova (SNIa) host galaxies affect the dark-energy parameter constraints in a small but very specific way: the parameters are biased in a single direction in parameter space that is a-priori knowable for a given SNIa dataset. We demonstrate the latter fact with a combination of inference from a cosmological N-body simulation with overwhelming statistics applied to the Pantheon SNIa data set, then confirm it by simple quantitative arguments. We quantify small modifications to the current analyses that would ensure that the effect of cosmological parameters is e…
In an isotropic and homogeneous Hubble expansion, all transverse motion is peculiar. Like the radial peculiar velocities of galaxies, transverse peculiar velocities are a means to trace the density of matter that does not rely on light tracing mass. Unlike radial peculiar velocity measurements that require precise redshift-independent distances in order to distinguish between the Hubble expansion and the observed redshift, transverse peculiar velocities can be measured using redshifts alone as a proxy for distance. Extragalactic proper motions can therefore directly measure peculiar velocities…
We consider a universe filled with perfect fluid with the constant equation of state parameter $ω$. In the theory of scalar perturbations, we study the effect of peculiar velocities on the gravitational potential. For radiation with $ω=1/3$, we obtain the expression for the gravitational potential in the integral form. Numerical calculation clearly demonstrates the modulation of the gravitational potential by acoustic oscillations due to the presence of peculiar velocities. We also show that peculiar velocities affect the gravitational potential in the case of the frustrated network of cosmic …
The Sunyaev-Zel'dolvich (SZ) effect is expected to be instrumental in measuring velocities of distant clusters in near future telescope surveys. We simplify the calculation of peculiar velocities of galaxy clusters using deep learning frameworks trained on numerical simulations to avoid the estimation of the optical depth. The image of distorted photon backgrounds are generated for idealized observations using one of the largest cosmological hydrodynamical simulations, the Magneticum simulations. The model is tested to be capable peculiar velocities from future kinetic SZ observations under di…
We propose a novel approach to accurately pin down the systematics due to the peculiar velocities of galaxies in measuring the Hubble constant from nearby galaxies in current and future gravitational-wave (GW) standard-siren experiments. Given the precision that future GW standard-siren experiments aim to achieve, the peculiar velocities of nearby galaxies will be a major source of uncertainty. Unlike the conventional backward reconstruction that requires additional redshift-independent distance indicators to recover the peculiar velocity field, we forwardly model the peculiar velocity field b…
Peculiar velocities are a precious tool to study the large-scale distribution of matter in the local universe and test cosmological models. However, present measurements of peculiar velocities are based on empirical distance indicators, which introduce large error bars. Here we present a new method to measure the peculiar velocities, by directly estimating luminosity distances through waveform signals from inspiralling compact binaries and measuring redshifts from electromagnetic (EM) counterparts. In the future, with the distance uncertainty of GW events reducing to $0.1$ per cent by future G…
We explore how information in images of nearby galaxies can be used to estimate their distance. We train a convolutional Neural Network (NN) to do this, using galaxy images from the Illustris simulation. We show that if the NN is trained on data with random errors added to the true distance (representing training using spectroscopic redshift instead of actual distance), then the NN can predict distances in a test dataset with greater accuracy than it was given in the training set. This is not unusual, as often NNs are trained on data with added noise, in order to increase robustness. In this c…
Peculiar motion introduces systematic variations in the observed luminosity distribution of galaxies. This allows one to constrain the cosmic peculiar velocity field from large galaxy redshift surveys. Using around half a million galaxies from the SDSS Data Release 7 at z ~ 0.1, we demonstrate the applicability of this approach to large datasets and obtain bounds on peculiar velocity moments and $σ_{8}$, the amplitude of the linear matter power spectrum. Our results are in good agreement with the $Λ$CDM model and consistent with the previously reported ~ 1% zero-point tilt in the SDSS photomet…
The problem of the reconstruction of the large scale density and velocity fields from peculiar velocities surveys is addressed here within a Bayesian framework by means of Hamiltonian Monte Carlo (HMC) sampling. The HAmiltonian Monte carlo reconstruction of the Local EnvironmenT (Hamlet) algorithm is designed to reconstruct the linear large scale density and velocity fields in conjunction with the undoing of lognormal bias in the derived distances and velocities of peculiar velocities surveys such as the Cosmicflows data. The Hamlet code has been tested against Cosmicflows mock catalogs consis…
It is known that the large-scale structure (LSS) mapped by a galaxy redshift survey is subject to distortions by galaxies' peculiar velocities. Besides the signatures generated in common N-point statistics, such as the anisotropy in the galaxy 2-point correlation function, the peculiar velocities also induce distinct features in LSS's morphological properties, which are fully described by four Minkowski functionals (MFs), i.e., the volume, surface area, integrated mean curvature and Euler characteristic (or genus). In this work, by using large suite of N-body simulations, we present and analyz…
Large-scale peculiar motions are commonplace in our universe. Nevertheless, their origin, evolution and implications are still largely unknown. It is generally assumed that bulk motions are a relatively recent addition to the universal kinematics, triggered by the increasing inhomogeneity and anisotropy of the post-recombination epoch. In this work, we focus on the linear evolution of peculiar velocities prior to recombination, namely in the late radiation era and also during a phase of de Sitter inflation. We begin by showing/confirming that bulk motions are triggered and sustained by the non…
We investigate the effect of peculiar velocities of inhomogeneities and the spatial curvature of the universe on the shape of the gravitational potential. To this end, we consider scalar perturbations of the FLRW metric. The gravitational potential satisfies a Helmholtz-type equation which follows from the system of linearized Einstein equations. We obtain analytical solutions of this equation in the cases of open and closed universes, filled with cold dark matter in presence of the cosmological constant. We demonstrate that, first, peculiar velocities significantly affect the screening length…
The peculiar velocity field offers a unique way to probe dark matter density field on large scales at low redshifts. In this work, we have compiled a new sample of 465 peculiar velocities from low redshift $(z < 0.067)$ Type Ia supernovae. We compare the reconstructed velocity field derived from the 2M++ galaxy redshift compilation to the supernovae, the SFI++ and the 2MTF Tully-Fisher distance catalogues. We used a forward method to jointly infer the distances and the velocities of distance indicators by comparing the observations to the reconstruction. Comparison of the reconstructed peculia…
The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as `wide angle' effects in redshift space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work we study how wide-angle effects modify the …
The increasing sensitivity of current experiments, which nowadays routinely measure the thermal SZ effect within galaxy clusters, provide the hope that peculiar velocities of individual clusters of galaxies will be measured rather soon using the kinematic SZ effect. Also next generation of X-ray telescopes with microcalorimeters, promise first detections of the motion of the intra cluster medium (ICM) within clusters. We used a large set of cosmological, hydrodynamical simulations, which cover very large cosmological volume, hosting a large number of rich clusters of galaxies, as well as moder…
This article explores three usual estimators, noted as $v_{12}$ of the pairwise velocity, $ψ_1$ and $ψ_2$ of the observed two-point galaxy peculiar velocity correlation functions. These estimators are tested on mock samples of {\it Cosmicflows-3} dataset \citep{Tully:2016aa} , derived from a numerical cosmological simulation, and also on a number of constrained realizations of this dataset. Observational measurements errors and cosmic variance are taken into consideration in the study. The result is a local measurement of $f σ_8 = 0.43 \left( \pm 0.03 \right)_\mathrm{obs} \left( \pm 0.11 \righ…
Cosmological peculiar velocities in general relativity
Queen Mary University of London（伦敦大学玛丽女王学院）；University of the Western Cape（西开普敦大学）；National Institute for Theoretical & Computational Sciences（理论与计算科学国家研究所）
We show that peculiar velocities of Type Ia supernovae can be used to derive constraints on the sum of neutrino masses, $Σm_ν$, and dark energy equation of state, $w = w_0+w_a(1-a)$, from measurements of the magnitude-redshift relation, complementary to galaxy redshift and weak lensing surveys. Light from a supernova propagates through a perturbed Universe so the luminosity distance is modified from its homogeneous prediction. This modification is proportional to the matter density fluctuation and its time derivative due to gravitational lensing and peculiar velocity respectively. At low redsh…
We propose a new method to recover the cosmological initial conditions of the presently observed galaxy distribution, which can serve to run constrained simulations of the Local Universe. Our method, the Reverse Zeldovich Approximation (RZA), can be applied to radial galaxy peculiar velocity data and extends the previously used Constrained Realizations (CR) method by adding a Lagrangian reconstruction step. The RZA method consists of applying the Zeldovich approximation in reverse to galaxy peculiar velocities to estimate the cosmic displacement field and the initial linear matter distribution…
When measuring the value of the Hubble parameter, $H_0$, it is necessary to know the recession velocity free of the effects of peculiar velocities. In this work, we study different models of peculiar velocity in the local Universe. In particular, we compare models based on density reconstruction from galaxy redshift surveys and kernel smoothing of peculiar velocity data. The velocity field from the density reconstruction is obtained using the 2M++ galaxy redshift compilation, which is compared to two adaptive kernel-smoothed velocity fields: the first obtained from the 6dF Fundamental Plane sa…
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 $β= 0.289^{+0.044}_{-0.043} \rm{(stat)} \pm 0.049 \rm{(…
We study the compression of information present in the correlated perturbations to the luminosity distance in the low-redshift ($z<0.1$) supernovae Ia due to peculiar velocities of these supernovae. We demonstrate that the naïve compression into angular velocity power spectrum does not work efficiently, due to thickness of the spherical shell over which the supernovae are measured. Instead, we show that measurements can be compressed into measurements of $f^2P(k)$, where $f$ is the logarithmic rate of growth of linear perturbations and $P(k)$ is their power spectrum. We develop an optimal quad…
We study the scale and redshift dependence of the power spectra for density perturbations and peculiar velocities, and the evolution of a coarse grained phase space density for (WDM) particles that decoupled during the radiation dominated stage. The (WDM) corrections are obtained in a perturbative expansion valid in the range of redshifts at which N-body simulations set up initial conditions, and for a wide range of scales. The redshift dependence is determined by the kurtosis $β_2$ of the distribution function at decoupling. At large redshift there is an enhancement of peculiar velocities for…
We present an analysis of peculiar velocities and their effect on supernova cosmology. In particular, we study (a) the corrections due to our own motion, (b) the effects of correlations in peculiar velocities induced by large-scale structure, and (c) uncertainties arising from a possible local under- or over-density. For all of these effects we present a case study of their impact on the cosmology derived by the Sloan Digital Sky Survey-II Supernova Survey (SDSS-II SN Survey). Correcting supernova redshifts for the CMB dipole slightly over-corrects nearby supernovae that share some of our loca…
Dust extinction and stellar confusion of the Milky Way hinder the detection of galaxies at low Galactic latitude, creating the so-called Zone of Avoidance (ZoA). This has hampered our understanding of the local dynamics, cosmic flow fields and the origin of the Cosmic Microwave Background dipole. The ZoA ($|b| \le 5^\circ$) is also excluded from the "whole-sky" Two Micron All-Sky Survey (2MASS) Redshift Survey (2MRS) and 2MASS Tully-Fisher Survey (2MTF). The latter aims to provide distances and peculiar velocities for all bright inclined 2MASS galaxies with $K_s^o$ $\leq 11\hbox{$.\!\!^{\rm m}…
Galaxy peculiar velocities provide an integral source of cosmological information that can be harnessed to measure the growth rate of large scale structure and constrain possible extensions to General Relativity. In this work, we present a method for extracting the information contained within galaxy peculiar velocities through an ensemble of direct peculiar velocity and galaxy clustering correlation statistics, including the effects of redshift space distortions, using data from the 6-degree Field Galaxy Survey. Our method compares the auto- and cross-correlation function multipoles of these …
Peculiar velocity measurements are the only tool available in the low-redshift Universe for mapping the large-scale distribution of matter and can thus be used to constrain cosmology. Using redshifts from the 2M++ redshift compilation, we reconstruct the density of galaxies within 200 Mpc/h, allowing for the first time good sampling of important superclusters such as the Shapley Concentration. We compare the predicted peculiar velocities from 2M++ to Tully-Fisher and SNe peculiar velocities. We find a value of $β^* \equiv Ω_{\rm{m}}^{0.55}/b^* = 0.431 \pm 0.021$, suggesting $Ω_{\rm{m}}^{0.55}σ…
The mounting evidence for anomalously large peculiar velocities in our Universe presents a challenge for the LCDM paradigm. The recent estimates of the large scale bulk flow by Watkins et al. are inconsistent at the nearly 3 sigma level with LCDM predictions. Meanwhile, Lee and Komatsu have recently estimated that the occurrence of high-velocity merging systems such as the Bullet Cluster (1E0657-57) is unlikely at a 6.5-5.8 sigma level, with an estimated probability between 3.3x10^{-11} and 3.6x10^{-9} in LCDM cosmology. We show that these anomalies are alleviated in a broad class of infrared-…
In this paper we investigate how observational effects could possibly bias cosmological inferences from peculiar velocity measurements. Specifically, we look at how bulk flow measurements are compared with theoretical predictions. Usually bulk flow calculations try to approximate the flow that would occur in a sphere around the observer. Using the Horizon Run 2 simulation we show that the traditional methods for bulk flow estimation can overestimate the magnitude of the bulk flow for two reasons: when the survey geometry is not spherical (the data do not cover the whole sky), and when the obse…
The theoretical basis of dark energy remains unknown and could signify a need to modify the laws of gravity on cosmological scales. In this study we investigate how the clustering and motions of galaxies can be used as probes of modified gravity theories, using galaxy and direct peculiar velocity auto- and cross-correlation functions. We measure and fit these correlation functions in simulations of $Λ$CDM, DGP, and $f(R)$ cosmologies and, by extracting the characteristic parameters of each model, we show that these theories can be distinguished from General Relativity using these measurements.…
Surveys of galaxy distances and radial peculiar velocities can be used to reconstruct the large scale structure. Other than systematic errors in the zero-point calibration of the galaxy distances the main source of uncertainties of such data are errors on the distance moduli, assumed here to be Gaussian and thus turn into lognormal errors on distances and velocities. Naively treated, it leads to spurious nearby outflow and strong infall at larger distances. The lognormal bias is corrected here and tested against mock data extracted from a $Λ$CDM simulation, designed to statistically follow the…
In this work we investigate the systematic uncertainties that arise from the calculation of the peculiar velocity when estimating the Hubble constant ($H_0$) from gravitational wave standard sirens. We study the GW170817 event and the estimation of the peculiar velocity of its host galaxy, NGC 4993, when using Gaussian smoothing over nearby galaxies. NGC 4993 being a relatively nearby galaxy, at $\sim 40 \ {\rm Mpc}$ away, is subject to a significant effect of peculiar velocities. We demonstrate a direct dependence of the estimated peculiar velocity value on the choice of smoothing scale. We s…
We propose to use the flux variability of lensed quasar images induced by gravitational microlensing to measure the transverse peculiar velocity of lens galaxies over a wide range of redshift. Microlensing variability is caused by the motions of the observer, the lens galaxy (including the motion of the stars within the galaxy), and the source; hence, its frequency is directly related to the galaxy's transverse peculiar velocity. The idea is to count time-event rates (e.g., peak or caustic crossing rates) in the observed microlensing light curves of lensed quasars that can be compared with mod…
We present a forward-modelled velocity field reconstruction algorithm that performs the reconstruction of the mass density field using only peculiar velocity data. Our method consistently accounts for the inhomogeneous Malmquist bias using analytic integration along the line-of-sight. By testing our method on a simulation, we show that our method gives an unbiased reconstruction of the velocity field. We show that not accounting for the inhomogeneous Malmquist bias can lead to significant biases in the forward-modelled reconstructions. We applied our method to a peculiar velocity data set cons…
Upcoming imaging surveys such as the Large Synoptic Survey Telescope will repeatedly scan large areas of sky and have the potential to yield million-supernova catalogs. Type Ia supernovae are excellent standard candles and will provide distance measures that suffice to detect mean pairwise velocities of their host galaxies. We show that when combining these distance measures with photometric redshifts for either the supernovae or their host galaxies, the mean pairwise velocities of the host galaxies will provide a dark energy probe which is competitive with other widely discussed methods. Addi…
A valuable amount of information is available in peculiar velocities of galaxies. Peculiar velocity surveys have recently allowed the discovery of potential problems with LCDM. Nonetheless, their direct observation through distance measurements remains a daunting task. Another way of considering the problem is to use orbit reconstruction methods assuming some mass-to-light assignment for galaxies. We give here two applications of this procedure for the study of large-scale bulk flows and the dynamics of voids in the Local Universe. We concentrate our study on the use of the Monge-Ampere-Kantor…
The discrepancy between estimates of the Hubble Constant ($H_0$) measured from local ($z \lesssim 0.1$) scales and from scales of the sound horizon is a crucial problem in modern cosmology. Peculiar velocities ($v_{pec}$) of standard candle distance indicators can systematically affect local $H_0$ measurements. We here use 2MRS galaxies to measure the local galaxy density field, finding a notable $z$ < 0.05 under-density in the SGC-6dFGS region of 27 $\pm$ 2 %. However, no strong evidence for a 'Local Void' pertaining to the full 2MRS sky coverage is found. Galaxy densities are used to measure…
Direct measurements of peculiar velocities of galaxies and clusters of galaxies can in principle provide explicit information on the three dimensional mass distribution, but this information is modulated by the fact that velocity field is sampled at galaxy positions, and is thus probing galaxy momentum. We derive expressions for the cross power spectrum between the density and momentum field and the auto spectrum of the momentum field in redshift space, by extending the distribution function method to these statistics. The resulting momentum cross and auto power spectra in redshift space are e…
We re-analyze data from the gravitational-wave event GW170817 and its host galaxy NGC4993 to demonstrate the importance of accurate total and peculiar velocities when measuring the Hubble constant using this nearby Standard Siren. We show that a number of reasonable choices can be made to estimate the velocities for this event, but that systematic differences remain between these measurements depending on the data used. This leads to significant changes in the Hubble constant inferred from GW170817. We present Bayesian Model Averaging as one way to account for these differences, and obtain $H_…
