Annu. Rev. Astron. Astrophys. 1994. 32: 371-418
Copyright © 1994 by . All rights reserved

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The editors suggested a review entitled ``Are There Large-Scale Motions in the Universe?''. The answer is ``yes'', in the sense that the interpretation of the data as motions is the simplest model, so far consistent with all other available data under the current ``standard model'' of physical cosmology. I will review tests which could have ended up falsifying this model and failed, but the scope of this review is much extended as the field has developed far beyond the question of existence of motions. Having adopted the motions as a working hypothesis, the study of large-scale dynamics is becoming a mature scientific field where observation and theory are confronted in a quantitative way. It is this area of major activity in cosmology that is addressed here.

I have made no attempt to provide a complete reference list, nor have I tried a balanced discussion of all the issues of relevance and all the authors involved. My goal is to provide a critical account of some of the issues which I find important, with emphasis on theoretical implications. In many cases I am not careful in giving proper credit by quoting only a recent paper automatically implying ``and references therein''. The reader is referred to a comprehensive, observation-oriented review of large-scale motions in historical perspective by Burstein (1990b), a detailed review of distance indicators in a collection of essays by Jacoby et al. (1992), and to Principles of Physical Cosmology by Peebles (1993). I apologize for tending to describe in more detail work which I was involved in and therefore know better.

The current phase of the field was seeded by two major developments. One was the confirmation of the dipole moment in the Cosmic Microwave Background (CMB) (Corey & Wilkinson 1976; Smoot et al. 1977), indicating via Doppler shift that the Local Group of galaxies (LG) is moving at ~ 600 km s-1 relative to the cosmological frame defined by the CMB. The other was the invention of methods for inferring distances independent of redshifts based on intrinsic relations between galaxy quantities (Section 3; Tully & Fisher 1977, TF; Faber & Jackson 1976, FJ). The radial peculiar velocity of a galaxy (the ``velocity'' u) is the difference between its total radial velocity as read from the redshift (the ``redshift'' z) and the Hubble velocity at its true distance (the ``distance'' r). Improved versions of these methods reduced the distance errors to the level of 15-21% which, with several hundred measured galaxies across the sky, enabled modeling the large-scale velocity field in terms of few-parameter ``toy'' models (Section 4.1), starting with a Virgo-centric infall (Aaronson et al. 1982b) and ending with spherical infall into a ``Great Attractor'' (GA, Lynden-Bell et al. 1988). The finding by the ``seven samurai'' (7S, Burstein et al. 1986) that the LG participates in a large streaming motion launched the present high-profile activity in this field. The toy modeling is gradually being replaced by non-parametric methods, where the full velocity field is reconstructed based on properties of gravitational flows (Section 4) and the associated mass-density fluctuation field is recovered from the spatial velocity derivatives (Section 2). With no simplified geometry imposed, the motions are not associated with single specific ``sources"; the gravitational acceleration is an integral of a continuous density field consisting of swells and troughs simultaneously pulling and pushing.

A parallel major development has been of all-sky magnitude-limited redshift surveys with many thousands of galaxies, starting with the CfA and SSRS optical surveys and continuing with the very useful recent surveys based on the IRAS satellite (Section 5). The large-scale inhomogeneity in the galaxy distribution (e.g. de Lapparent et al. 1986) provided a clear hint for associated motions. An all-sky redshift survey can be converted into a galaxy-density field and then integrated to derive a predicted velocity field under the assumption of gravity and a certain ``biasing'' relation between galaxies and mass. The comparison of the fields obtained from redshifts to those obtained from velocities is at the heart of the research of large-scale structure (LSS), and the results carry major implications (Sections 6.2, 8.2).

Data of both types are rapidly accumulating, and a major effort is directed at reducing the errors and carefully estimating those which remain, to enable quantitative testing of LSS formation theories. The standard theory consists of several working hypotheses which one tries to falsify by the observations or, if found consistent, to determine the characteristic model parameters. The hypotheses, which will be elaborated on later, can be listed as follows:

H1. The background cosmology is the standard homogeneous Friedman Robertson Walker model, possibly with an Inflation phase, where the CMB defines a cosmological ``rest frame''. If so, then one wishes to determine the cosmological density parameter Omega (and the cosmological constant Lambda and the Hubble constant H).
H2. The structure originated from a random field of small-amplitude initial density fluctuations. If so, the goal is to find out whether they were Gaussian, whether the power spectrum (PS) was scale-invariant (power index n = 1), and whether the energy density was perturbed adiabatically or in an isocurvature manner.
H3. The spectrum of fluctuations was filtered during the radiation-plasma era in a way characteristic of the nature of the dark matter (DM) which dominates the mass density. The DM could be baryonic or non-baryonic. If non-baryonic it could be ``hot'' or ``cold'' depending on when it became non-relativistic.
H4. The fluctuations grew by gravitational instability (GI) into the present LSS. This is a sufficient but not necessary condition for:
  1. The quasi-linear velocity field smoothed over a sufficiently-large scale is irrotational.
  2. The galaxies trace a unique underlying velocity field, apart from possible ``velocity bias'' of ~ 10% on small scales.
H5. The density fluctuations of visible galaxies are correlated with the underlying mass fluctuations. If this relation is roughly linear, then the linearized continuity equation in GI implies a relation between velocity and galaxy density. If so, the characteristic parameter is the density-biasing factor b.
H6. The TF and Dn - sigma methods measure true distances, which allow the reconstruction of a large-scale velocity field with known systematic biases under control.

This review is geared toward the confrontation of observations with these hypotheses. The relevant observations can be classified into the following three major categories:

O1. Angular fluctuations in the CMB temperature at various angular scales.

O2. The distribution of luminous objects on the sky and in redshift space.

O3. Peculiar velocities of galaxies along the line of sight.

Note that O1 and O3 are related to dynamical ingredients H1-4 and H6, bypassing the uncertain nature of galaxy-density biasing H5. Also, O1 and O2 refer to the theory independently of H4a,b and H6, which address the velocities and their analysis.

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