Large-scale Peculiar Velocity Field Research Articles

Velocity reconstruction with the cosmic microwave background and galaxy surveys

The kinetic Sunyaev Zel'dovich (kSZ) and moving lens effects, secondary contributions to the cosmic microwave background (CMB), carry significant cosmological information due to their dependence on the large-scale peculiar velocity field. Previous work identified a promising means of extracting this cosmological information using a set of quadratic estimators for the radial and transverse components of the velocity field. These estimators are based on the statistically anisotropic components of the cross-correlation between the CMB and a tracer of large scale structure, such as a galaxy redshift survey. In this work, we assess the challenges to the program of velocity reconstruction posed by various foregrounds and systematics in the CMB and galaxy surveys, as well as biases in the quadratic estimators. To do so, we further develop the quadratic estimator formalism and implement a numerical code for computing properly correlated spectra for all the components of the CMB (primary/secondary blackbody components and foregrounds) and a photometric redshift survey, with associated redshift errors, to allow for accurate forecasting. We create a simulation framework for generating realizations of properly correlated CMB maps and redshift binned galaxy number counts, assuming the underlying fields are Gaussian, and use this to validate a velocity reconstruction pipeline and assess map-based systematics such as masking. We highlight the most significant challenges for velocity reconstruction, which include biases associated with: modelling errors, characterization of redshift errors, and coarse graining of cosmological fields on our past light cone. Despite these challenges, the outlook for velocity reconstruction is quite optimistic, and we use our reconstruction pipeline to confirm that these techniques will be feasible with near-term CMB experiments and photometric galaxy redshift surveys.

Large-scale peculiar velocity fields: Newtonian vs relativistic treatment

We employ a perturbative analysis to study the evolution of large-scale peculiar velocity fields within the framework of Newtonian gravity and then compare our results to those of the corresponding relativistic treatment. In so doing, we use the same mathematical formalism and apply the same physical approach. This facilitates a direct and transparent comparison between the two treatments. Our study recovers and extends the familiar Newtonian results on the one hand, while on the other it shows that the Newtonian analysis leads to substantially weaker growth-rates for the peculiar velocity field, compared to the relativistic approach. This implies that, by using Newton's rather than Einstein's theory, one could seriously underestimate the overall kinematic evolution of cosmological peculiar motions. We are also in the position to identify the reason the two theories arrive at such considerably different results and conclusions.

Iterative removal of redshift-space distortions from galaxy clustering

ABSTRACT Observations of galaxy clustering are made in redshift space, which results in distortions to the underlying isotropic distribution of galaxies. These redshift-space distortions (RSDs) 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 non-linear 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 able to recover the real-space galaxy correlation function with an accuracy of $\sim \!1{{\ \rm per\ cent}}$, and restore the quadrupole accurately to 0, on scales $s\gtrsim 20\,h^{-1}\, {\rm Mpc}$. It also leads to an improvement in the reconstruction of the initial density field, which could help to accurately locate the BAO peaks. An ‘internal calibration’ scheme is proposed to determine the values of cosmological parameters, as a part of the reconstruction process, and possibilities to break parameter degeneracies are discussed. RSD reconstruction can offer a potential way to simultaneously extract the cosmological parameters, initial density field, real-space galaxy positions, and large-scale peculiar velocity field (of the real Universe), making it an alternative to standard perturbative approaches in galaxy clustering analysis, bypassing the need for RSD modelling.

Speed from light: growth rate and bulk flow at z ∼ 0.1 from improved SDSS DR13 photometry

Observed galaxy luminosities (derived from redshifts) hold information on the large-scale peculiar velocity field in the form of spatially correlated scatter, which allows for bounds on bulk flows and the growth rate of matter density perturbations using large galaxy redshift surveys. We apply this luminosity approach to galaxies from the recent SDSS Data Release 13. Our goal is twofold. First, we take advantage of the recalibrated photometry to identify possible systematic errors relevant to our previous analysis of earlier data. Second, we seek improved constraints on the bulk flow and the normalized growth rate f$\sigma_{8}$ at z ~ 0.1. Our results confirm the robustness of our method. Bulk flow amplitudes, estimated in two redshift bins with 0.02 < z$_{1}$ < 0.07 < z$_{2}$ < 0.22, are generally smaller than in previous measurements, consistent with both the updated photometry and expectations for the $\Lambda$CDM model. The obtained growth rate, f$\sigma_{8}$ = 0.48 +/- 0.16, is larger than, but still compatible with, its previous estimate, and closer to the reference value of Planck. Rather than precision, the importance of these results is due to the fact that they follow from an independent method that relies on accurate photometry, which is a top requirement for next-generation photometric catalogs.

An unbiased estimator of peculiar velocity with Gaussian distributed errors for precision cosmology

We introduce a new estimator of the peculiar velocity of a galaxy or group of galaxies from redshift and distance estimates. This estimator results in peculiar velocity estimates which are statistically unbiased and that have errors that are Gaussian distributed, thus meeting the assumptions of analyses that rely on individual peculiar velocities. We apply this estimator to the SFI++ and the Cosmicflows-2 catalogs of galaxy distances and, using the fact that peculiar velocity estimates of distant galaxies are error dominated, examine their error distributions, The adoption of the new estimator significantly improves the accuracy and validity of studies of the large-scale peculiar velocity field and eliminates potential systematic biases, thus helping to bring peculiar velocity analysis into the era of precision cosmology. In addition, our method of examining the distribution of velocity errors should provide a useful check of the statistics of large peculiar velocity catalogs, particularly those that are compiled out of data from multiple sources.

Cosmic flows on 100 h−1 Mpc scales: standardized minimum variance bulk flow, shear and octupole moments

The low order moments, such as the bulk flow and shear, of the large scale peculiar velocity field are sensitive probes of the matter density fluctuations on very large scales. In practice, however, peculiar velocity surveys are usually sparse and noisy, which can lead to the aliasing of small scale power into what is meant to be a probe of the largest scales. Previously, we developed an optimal ``minimum variance'' (MV) weighting scheme, designed to overcome this problem by minimizing the difference between the measured bulk flow (BF) and that which would be measured by an ideal survey. Here we extend this MV analysis to include the shear and octupole moments, which are designed to have almost no correlations between them so that they are virtually orthogonal. We apply this MV analysis to a compilation of all major peculiar velocity surveys, consisting of 4536 measurements. Our estimate of the BF on scales of ~ 100 Mpc/h has a magnitude of |v|= 416 +/- 78 km/s towards Galactic l = 282 degree +/- 11 degree and b = 6 degree +/- 6 degree. This result is in disagreement with LCDM with WMAP5 cosmological parameters at a high confidence level, but is in good agreement with our previous MV result without an orthogonality constraint, showing that the shear and octupole moments did not contaminate the previous BF measurement. The shear and octupole moments are consistent with WMAP5 power spectrum, although the measurement noise is larger for these moments than for the BF. The relatively low shear moments suggest that the sources responsible for the BF are at large distances.

Observational biases in Lagrangian reconstructions of cosmic velocity fields

Lagrangian reconstruction of large-scale peculiar velocity fields can be strongly affected by observational biases. We develop a thorough analysis of these systematic effects by relying on specially selected mock catalogues. For the purpose of this paper, we use the MAK reconstruction method, although any other Lagrangian reconstruction method should be sensitive to the same problems. We extensively study the uncertainty in the mass-to-light assignment due to luminosity incompleteness, and the poorly-determined relation between mass and luminosity. The impact of redshift distortion corrections is analyzed in the context of MAK and we check the importance of edge and finite-volume effects on the reconstructed velocities. Using three mock catalogues with different average densities, we also study the effect of cosmic variance. In particular, one of them presents the same global features as found in observational catalogues that extend to 80 Mpc/h scales. We give recipes, checked using the aforementioned mock catalogues, to handle these particular observational effects, after having introduced them into the mock catalogues so as to quantitatively mimic the most densely sampled currently available galaxy catalogue of the nearby universe. Once biases have been taken care of, the typical resulting error in reconstructed velocities is typically about a quarter of the overall velocity dispersion, and without significant bias. We finally model our reconstruction errors to propose an improved Bayesian approach to measure Omega_m in an unbiased way by comparing the reconstructed velocities to the measured ones in distance space, even though they may be plagued by large errors. We show that, in the context of observational data, a nearly unbiased estimator of Omega_m may be built using MAK reconstruction.

Power Spectrum of Cosmic Momentum Field Measured from the SFI Galaxy Sample

We have measured the cosmic momentum power spectrum from the peculiar velocities of galaxies in the SFI sample. The SFI catalog contains field spiral galaxies with radial peculiar velocities derived from the I-band Tully-Fisher relation. As a natural measure of the large-scale peculiar velocity field, we use the cosmic momentum field that is defined as the peculiar velocity field weighted by local number of galaxies. We have shown that the momentum power spectrum can be derived from the density power spectrum for the constant linear biasing of galaxy formation, which makes it possible to estimate \beta_S = \Omega_m^{0.6} / b_S parameter precisely where \Omega_m is the matter density parameter and b_S is the bias factor for optical spiral galaxies. At each wavenumber k we estimate \beta_S(k) as the ratio of the measured to the derived momentum power over a wide range of scales (0.026 h^{-1}Mpc <~ k <~ 0.157 h^{-1}Mpc) that spans the linear to the quasi-linear regimes. The estimated \beta_S(k)'s have stable values around 0.5, which demonstrates the constancy of \beta_S parameter at scales down to 40 h^{-1}Mpc. We have obtained \beta_S=0.49_{-0.05}^{+0.08} or \Omega_m = 0.30_{-0.05}^{+0.09} b_S^{5/3}, and the amplitude of mass fluctuation as \sigma_8\Omega_m^{0.6}=0.56_{-0.21}^{+0.27}. The 68% confidence limits include the cosmic variance. We have also estimated the mass density power spectrum. For example, at k=0.1047 h Mpc^{-1} (\lambda=60 h^{-1}Mpc) we measure \Omega_m^{1.2} P_{\delta}(k)=(2.51_{-0.94}^{+0.91})\times 10^3 (h^{-1}Mpc)^3, which is lower compared to the high-amplitude power spectra found from the previous maximum likelihood analyses of peculiar velocity samples like Mark III, SFI, and ENEAR.

Cosmic momentum field and mass fluctuation power spectrum

We introduce the cosmic momentum field as a new measure of the large-scale peculiar velocity and matter fluctuation fields. The momentum field is defined as the peculiar velocity field traced and weighted by galaxies, and is equal to the velocity field in the linear regime. We show that the radial component of the momentum field can be considered as a scalar field with the power spectrum which is practically one-third of that of the total momentum field. We present a formula for the power spectrum directly calculable from the observed radial peculiar velocity data. The momentum power spectrum is measured for the MAT sample in the Mark III catalogue of peculiar velocities of galaxies. Using the momentum power spectrum we find the amplitude of the matter power spectrum is and at the wavenumbers 0.049 and 0.074 h Mpc−1, respectively, where Ω is the density parameter. The 68 per cent confidence limits include the cosmic variance. The measured momentum and density power spectra together indicate that the parameter or where bO is the bias factor for optical galaxies.

COBE ‐DMR–normalized Open Cold Dark Matter Cosmogonies

Cut-sky orthogonal mode analyses of the COBE-DMR 53 and 90 GHz sky maps are used to determine the normalization of a variety of open cosmogonical models based on the cold dark matter scenario. To constrain the allowed cosmological parameter range for these open cosmogonies, the predictions of the DMR-normalized models are compared to various observational measures of cosmography and large-scale structure, viz., the age of the universe; small-scale dynamical estimates of the clustered-mass density parameter ?0; constraints on the Hubble parameter h, the X-ray cluster baryonic-mass fraction ?B/?0, and the matter power spectrum shape parameter; estimates of the mass perturbation amplitude; and constraints on the large-scale peculiar velocity field. The open-bubble inflation model (Ratra & Peebles; Bucher, Goldhaber, & Turok; Yamamoto, Sasaki, & Tanaka) is consistent with current determinations of the 95% confidence level (c.l.) range of these observational constraints, provided 0.3 < ?0 0.6 (~95% c.l.). More specifically, for a range of h, the model is reasonably consistent with recent high-redshift estimates of the deuterium abundance that suggest ?Bh2 ~ 0.007, provided ?0 ~ 0.35; recent high-redshift estimates of the deuterium abundance that suggest ?Bh2 ~ 0.02 favor ?0 ~ 0.5, while the old nucleosynthesis value ?Bh2 = 0.0125 requires ?0 ~ 0.4. Small shifts in the inferred COBE-DMR normalization amplitudes due to (1) the small differences between the galactic- and ecliptic-coordinate sky maps, (2) the inclusion or exclusion of the quadrupole moment in the analysis, (3) the faint high-latitude Galactic emission treatment, and (4) the dependence of the theoretical cosmic microwave background anisotropy angular spectral shape on the value of h and ?B are explicitly quantified. Corresponding variations in the likelihood fits of models to the DMR data then imply that the DMR data alone do not possess sufficient discriminative power to prefer any values for ?0, h, or ?B at the 95% c.l. for the models considered. At a lower c.l., and when the quadrupole moment is included in the analysis, the DMR data are most consistent with either ?0 0.1 or ?0 ~ 0.7 (depending on the model considered). However, when the quadrupole moment is excluded from the analysis, the DMR data are most consistent with ?0 ~ 0.35-0.5 in all open models considered (with 0.1 ? ?0 ? 1), including the open-bubble inflation model. Earlier claims (Yamamoto & Bunn; Bunn & White) that the DMR data require a 95% c.l. lower bound on ?0 (~0.3) are not supported by our (complete) analysis of the 4 year data: the DMR data alone cannot be used to constrain ?0 meaningfully.

The Peculiar Motions of Early-Type Galaxies in Two Distant Regions. I. Cluster and Galaxy Selection

The EFAR project is a study of 736 candidate elliptical galaxies in 84 clusters lying in two regions towards Hercules-Corona Borealis and Perseus-Pisces-Cetus at distances cz = 6000-15000 km/s. In this paper (the first of a series) we present an introduction to the EFAR project and describe in detail the selection of the clusters and galaxies in our sample. Fundamental data for the galaxies and clusters are given, including accurate new positions for each galaxy and redshifts for each cluster. The galaxy selection functions are determined using diameters measured from Schmidt sky survey images for 2185 galaxies in the cluster fields. Future papers in this series will present the spectroscopic and photometric observations of this sample, investigate the properties of the fundamental plane for ellipticals, and determine the large-scale peculiar velocity fields in these two regions of the universe.

COMPARING LARGE-SCALE COSMOLOGICAL DENSITY FLUCTUATIONS

Abstract Two methods for looking at cosmological density on large scales are briefly described. The first takes galaxies observed in infrared, by the IRAS satellite. The second method, called POTENT by its inventors (Dekel and Bertschinger), uses the observed peculiar motions of galaxies to find the large scale peculiar velocity field. These two methods can be combined to test various theories of structure formation. First, though, we need to make sure that the velocity field derived from POTENT is consistent with the fractional overdensity field derived from IRAS. One way to compare them employs the non-parametric Wilcoxon-Mann-Whitney test.

CLUSTERING AND LARGE-SCALE STRUCTURE WITH THE SLOAN DIGITAL SKY SURVEY

ABSTRACT The Sloan Digital Sky Survey (SDSS) will provide a complete imaging and spectroscopic survey of the high-latitude northern sky. The 2D survey will image the sky in five colors and will contain nearly 5 x 107 galaxies to g ~23m. The spectroscopic survey will obtain spectra of the brightest 106 galaxies, 105 quasars, and 1035 rich clusters of galaxies (to g ~18.3-19.3m, respectively). I summarize some of the science opportunities that will be made possible by this survey for studying the clustering and large-scale structure of the universe. The survey will identify a complete sample of several thousand rich clusters of galaxies, both in 2D and 3D--the largest automated sample yet available. The extensive cluster sample can be used to determine critical clustering properties such as the luminoisty-function, velocity-function, and mass-function of clusters of galaxies (a critical test for cosmological models), detailed cluster dynamics and Omegadyn, the cluster correlation function and its dependence on richness, cluster evolution, superclustering and voids to the largest scales yet observed, the motions of clusters and their large-scale peculiar velocity field, as well as detailed correlations between x-ray and optical properties of clusters, the density-morphology relation, and cluster-quasar associations. The large redshift survey, reaching to a depth of >~600h-1 Mpc, will accurately map the largest scales yet observed, determine the power-spectrum and correlation function on these large scales for different type galaxies, and study the clustering of quasars to high redshifts (z >~ 4). The implications of the survey for cosmological models, the dark matter, and Omega are also discussed.

Large-scale motions in the universe: Using clusters of galaxies as tracers

Can clusters of galaxies be used to trace the large-scale peculiar velocity field of the universe? We answer this question by using large-scale cosmological simulations to compare the motions of rich clusters of galaxies with the motion of the underlying matter distribution. Three models are investigated: Omega = 1 and Omega = 0.3 cold dark matter (CDM), and Omega = 0.3 primeval baryonic isocurvature (PBI) models, all normalized to the Cosmic Background Explorer (COBE) background fluctuations. We compare the cluster and mass distribution of peculiar velocities, bulk motions, velocity dispersions, and Mach numbers as a function of scale for R greater than or = 50/h Mpc. We also present the large-scale velocity and potential maps of clusters and of the matter. We find that clusters of galaxies trace well the large-scale velocity field and can serve as an efficient tool to constrain cosmological models. The recently reported bulk motion of clusters 689 +/- 178 km/s on approximately 150/h Mpc scale (Lauer & Postman 1994) is larger than expected in any of the models studied (less than or = 190 +/- 78 km/s).

Large-Scale Peculiar Velocity Field Due to Infinitely Long Cosmic Strings

view Abstract Citations (9) References (26) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Large-Scale Peculiar Velocity Field Due to Infinitely Long Cosmic Strings Hara, Tetsuya ; Maehoenen, Petri ; Miyoshi, Shigeru Abstract We investigate the large-scale peculiar velocity field of dark matter due to the wakes formed by infinitely long cosmic strings. The peculiar velocity due to such strings, which passed through at the stage 1 + ζi is solved analytically for one-dimensional case, including the contribution of the background radiation density. The three dimensional large-scale peculiar velocities will be the vector sum of such velocities, and the root mean square (rms) peculiar velocities can be estimated. The large peculiar velocity of the Local Group (≃600 km s-1) and the distribution of peculiar velocities for nearby 20 clusters of galaxies can be explained by adopting the parameter Gμβγ(n)1/2 (4 ± 1) × 10-6, where μ and β are the line density and the velocity of a cosmic string in units of c = 1 and γ = (1 - β2)-1/2. The parameter n denotes the number of infinitely long cosmic strings per horizon passed through in each e-time expansion of the universe. Publication: The Astrophysical Journal Pub Date: October 1993 DOI: 10.1086/173176 Bibcode: 1993ApJ...415..445H Keywords: COSMOLOGY: THEORY; COSMOLOGY: DARK MATTER; COSMIC STRINGS; GALAXIES: DISTANCES AND REDSHIFTS; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE full text sources ADS | data products SIMBAD (1)

The large-scale velocity field beyond the local supercluster

view Abstract Citations (19) References (55) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Large-Scale Velocity Field beyond the Local Supercluster Han, Mingsheng Abstract Relative distances of 16 clusters of galaxies in the redshift range from 3000 to 11,000 km s^-1^ are measured using the I-band Tully-Fisher relation. Different techniques of deriving distances of clusters using a distance indicator are discussed and compared in regard to the sample selection bias. The large-scale peculiar velocity field as traced by our sample clusters is found to be highly nonrandom, and appears to be a coherent flow, in the cosmic microwave background (CMB) frame; the flow is towards the general direction of the "Great Attractor," with an amplitude of some 400-600 km s^-1^ at the position of the Local Group (LG). Publication: The Astrophysical Journal Pub Date: August 1992 DOI: 10.1086/171631 Bibcode: 1992ApJ...395...75H Keywords: Astrometry; Galactic Clusters; Local Group (Astronomy); Red Shift; Galactic Evolution; Relic Radiation; Velocity Distribution; Astrophysics; GALAXIES: CLUSTERING; GALAXIES: DISTANCES AND REDSHIFTS full text sources ADS | data products SIMBAD (17) NED (15)

Small-scale structure on cosmic strings and galaxy formation.

The density perturbations produced by cosmic strings in cold dark matter are examined using the Zel'dovich approximation. We use the results from recent numerical simulations which show that the strings have significant small-scale structure. It is shown that the string network produces wakelike overdensities which may be able to account for the observed large-scale structure of the Universe. In the process of producing wakes the strings also produce large-scale peculiar velocity fields. It is shown that these velocities are coherent over distances which are too small to account for the observed large-scale streaming motions. It is also shown that the small-scale structure on the strings can fragment the wakes into pieces which have the mass of a galaxy.

Large-scale peculiar velocity fields in superclusters of galaxies

view Abstract Citations (15) References (33) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Large-Scale Peculiar Velocity Fields in Superclusters of Galaxies Gavazzi, G. ; Scodeggio, M. ; Boselli, A. ; Trinchieri, G. Abstract The Tully-Fisher relation is used to derive distances of 262 galaxies in seven clusters. Care is taken to reduce possible causes of error in the distance determination and to evaluate sources of scatter in the distance-velocity relation. The scatter in Virgo, A262 (and possibly in the Coma and Hercules superclusters) is real and is evidence of large- scale (50 Mpc) peculiar velocity fields. In the Virgo region we confirm the existence of background galaxies infalling toward the cluster (see work by Pierce and Tully) and we find evidence for infalling foreground objects. The Cancer cluster is confirmed to be an unbound collection of groups (see work by Bothun et al.). The Hubble relation is linear from 0 to 13,000 km s^-1^ with H_0_= 90+/-17 km s^-1^ Mpc. Publication: The Astrophysical Journal Pub Date: November 1991 DOI: 10.1086/170688 Bibcode: 1991ApJ...382...19G Keywords: Galactic Clusters; H Lines; Velocity Distribution; Astronomical Catalogs; Calibrating; Charge Coupled Devices; Error Analysis; Astrophysics; COSMOLOGY; GALAXIES: CLUSTERING; GALAXIES: REDSHIFTS full text sources ADS | data products SIMBAD (22) NED (7)

Cosmic microwave anisotropies and large-scale velocity fields in isocurvature hot dark matter models

view Abstract Citations (15) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Cosmic Microwave Anisotropies and Large-Scale Velocity Fields in Isocurvature Hot Dark Matter Models Sugiyama, Naoshi ; Sasaki, Misao ; Tomita, Kenji Abstract We investigate the evolution of isocurvature density perturbations in a universe dominated by hot dark matter (HDM) and evaluate anisotropies in the cosmic microwave background and large-scale peculiar velocity fields. We find isocurvature HDM models are more viable than adiabatic HDM models in that the former can account for relatively large velocity fields on large scales while keeping the cosmic microwave background anisotropies below the observational upper limits as compared to the latter. However, isocurvature HDM models would still have difficulties if the actual velocity fields on scales >~ 50h^-1^ Mpc were confirmed to be substantially greater than ~400 km s^-1^. Publication: The Astrophysical Journal Pub Date: March 1989 DOI: 10.1086/185397 Bibcode: 1989ApJ...338L..45S Keywords: Astronomical Models; Background Radiation; Cosmology; Dark Matter; Microwaves; Perturbation Theory; Universe; Velocity Distribution; Astrophysics; COSMIC BACKGROUND RADIATION; COSMOLOGY; EARLY UNIVERSE full text sources ADS |

Cosmic strings: Large-scale mass fluctuations and velocity fields

In this paper we calculate the large scale mass fluctuations and peculiar velocity fields in the cosmic string scenario in different dark matter-dominated universes. By using Turok et al.'s string density fluctuation spectra before gravitational growth and the usual linear perturbation theory, we get the mean square root mass fluctuation 〈( δM M ) 2(M)〉 1 2 and obtain the first calculation of large-scale peculiar velocity fields in the cosmic string picture. If we assume galaxies trace the mass distribution, normalization of δM/ M at scale 8 Mpch −1 requires Gμ > 10 −5, which is too large to be allowed by Big Bang nucleosynthesis theory and the observed background radiation anisotropy, where μ is the mass per unit string length. Pancaking at z = 3 in neutrino-dominated universes requires even larger Gμ. The peculiar velocity decreases more slowly with increasing distance than in usual cosmological models, but this is still not enough to explain Collins et al.'s observed data. Our results indicate that cosmic string density fluctuations alone cannot form such large scale structures as observed.