arXiv:1001.1154v1 [astro-ph.CO] 8 Jan 2010 Statistical Determination of Bulk Flow Motions $^{1}$Yong-Seon Song, 1 , $^{2}$Cristiano G. Sabiu, $^{1}$Robert C. Nichol and $^{2}$Christopher J. Miller ∗ $^{1}$Institute of Cosmology & Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK $^{2}$Department of Physics & Astronomy, University College London, Gower Street, London, U.K $^{3}$Cerro-Tololo Inter-American Observatory, National Optical Astronomy Observatory, 950 North Cherry Ave., Tucson, AZ 85719, USA (Dated: November 10, 2018) We present here a new parameterization for the bulk motions of galaxies and clusters (in the linear regime) that can be measured statistically from the shape and amplitude of the two–dimensional two–point correlation function. We further propose the one–dimensional velocity dispersion ( v p ) of the bulk flow as a complementary measure of redshift–space distortions, which is model–independent and not dependent on the normalisation method. As a demonstration, we have applied our new methodology to the C4 cluster catalogue constructed from Data Release Three (DR3) of the Sloan Digital Sky Survey. We find v p = 270 +433 km/s (also consistent with v p = 0) for this cluster sample (at ¯ z = 0 . 1), which is in agreement with that predicted for a WMAP5–normalised ΛCDM model (i.e., v p (ΛCDM) = 203 km/s). This measurement does not lend support to recent claims of excessive bulk motions ( ≃ 1000 km/s) which appear in conflict with ΛCDM, although our large statistical error cannot rule them out. From the measured coherent evolution of v p , we develop a technique to re-construct the perturbed potential, as well as estimating the unbiased matter density fluctuations and scale–independent bias. effect on light as its trajectory is bent by the gravitational potential. Likewise, galaxies (and clusters of galaxies) measure the correlations amongst large–scale local inho- mogeneities, while the observed distortions in these cor- relations (in redshift–space) can be used to extract infor- mation about peculiar velocities [11–14]. In this paper, we explore the cosmological constraints on the physics of cosmic acceleration using peculiar velocities, as it is one of the key quantities required for a consistency test of General Relativity [15, 16]. In addition to using geometrical probes like Super- novae to constrain the cosmic acceleration, tests based on the formation of structures in the Universe also pro- vide a method for validating our cosmological models. In particular, we can investigate the consistency between the geometrical expansion history of the Universe and the evolution of local density inhomogeneities to help re- veal a deeper understanding of the nature of the cosmic acceleration [5–9]. A decade ago, astronomers discovered the expansion of the Universe was accelerating via the cosmological dimming of distant supernovae [1, 2]. Since then, the combination of numerous, and diverse, experiments has helped to establish the Cosmological Constant (specifi- cally a ΛCDM model) as the leading candidate to explain this cosmic acceleration. However, with no theoretical motivation to explain the required low energy vacuum of the ΛCDM model, there is no reason to preclude alter- native models, especially those based upon the possible violation of fundamental physics which have yet to be proven on cosmological scales [3, 4]. PACS numbers: draft In general, there are three observables that can be used to quantify structure formation in the Universe, namely geometrical perturbations, energy–momentum fluctua- tions and peculiar velocities, all of which will be measured to high precision via future experiments like DES, LSST, JDEM and Euclid (see details of these experiments in the recent FoMSWG report [10]). In more detail, such weak lensing experiments measure the integrated geometrical Given the importance of these large–scale bulk flow measurements, we propose here an alternative methodol- ogy to help check these recent claims of anomalously high peculiar velocities which are inconsistent with the stan- dard ΛCDM cosmology. We start by outlining a statis- tical determination of bulk flow motions using redshift– space distortions in large-scale galaxy or cluster surveys. Such redshift-space distortions are easily seen in the two– dimensional correlation function ( ξ$_{s}$ ( σ, π )), which is the Early observational studies of the peculiar velocity field, or “bulk flows”, have produced for many years dis- crepant results [17], primarily due to small sample sizes and the heterogeneous selection of galaxies. However, a recent re-analysis of these earlier surveys [18] has now provided a consistent observational picture from these data and finds significant evidence for a larger than ex- pected bulk motion. This is consistent with new mea- surements of the bulk motion of clusters of galaxies us- ing a completely different methodology[19, 20], which leads to the intriguing situation that all these measure- ments appear to be significantly greater in amplitude, and scale, than expected in a concordance, WMAP5– normalised ΛCDM cosmological model. Such discrepan- cies with ΛCDM may give support to exotic cosmological models like modified gravity [21]. I. INTRODUCTION ∗ Electronic address: yong-seon.song@port.ac.uk