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

*Are the motions real*?
The large-scale bulk flow rests upon the interpretation of the CMB
dipole as motion of the LG in the CMB frame, based on the assumption
of cosmological isotropy (H1), and supported by
the gravitational acceleration derived at the LG from the galaxy and mass
distribution around it (Section 6.1). The
detection of *T / T* ~
10^{-5} is a clear indication, via GI, for
~ 300 km s^{-1} motions over ~ 100 h^{-1}Mpc
(Section 6.1). While this is reassuring, the
LP hint for possible very-large coherence suggests caution
(Section 7.1).
Evidence that the
TF-inferred motions about the LG
are real (H6) are *(a)* the correlation _{g} - **·**
**v**, which
is robustly predicted for true velocities based on continuity and
would be hard to mimic by environmental effects
(Section 6.2),
*(b)* the failure to detect any significant correlation between
velocities and the environment or other galaxy properties
(Section 6.3), and
*(c)* the similarity between the velocity fields traced by spirals
(TF) and by ellipticals
(*D _{n}* - )
(Section 6.3).

Is *linear biasing* a good approximation (H5)?
The galaxy-velocity correlation is most sensitive to it,
and the observed correlation on scales 10 h^{-1}Mpc is
consistent with linear biasing properly modified in the tails
(Section 6.2).
However, it is difficult to distinguish non-linear biasing from
non-linear gravitational effects, and the range of different estimates
of
(Section 8) may indicate that the biasing
parameter varies
as a function of scale. The ratio of ~ 10 h^{-1}Mpc-smoothed
densities for optical and *IRAS* galaxies is *b*_{opt}
/ *b*_{I}
1.3-1.5.

Is *gravity* the dominant source of LSS (H4)?
The observed velocity-density correlation
(Section 6.2) is fully
consistent with GI, but it is sensitive to continuity more than
to the specific time dependence implied by gravity. Any non-GI process
followed by a gravitating phase would end up consistent with this
observation, and certain non-GI models may show a similar
spatial behavior even if gravity never plays any role.
The E-S correlation (Section 6.3) is also
consistent with gravity as galaxies of all types trace the same
velocity field (H4b), but any model where all galaxies are
set into motion by the same mechanism could pass this test.
The strongest evidence for gravitational origin comes from the
statistical agreement between the fluctuations of today and those implied by
the CMB at the time of recombination. A marginal warning signal for GI
is provided by the ~ 700 km s^{-1} bulk
velocity indicated by LP for rich clusters across ~ 200
h^{-1}Mpc. Such a velocity at face value would be in conflict with
the gravitational acceleration implied by the cluster distribution
and with the *T /
T* ~ 10^{-5} at ~ 2°, but the errors are large.

The property of *irrotationality* (H4a) used in the reconstruction
from either velocities or densities is impossible to deduce solely from
observations of velocities along the lines of sight from one origin.
Irrotationality is assumed based on the theory of GI, or it can be tested
against the assumption of isotropy by measuring the isotropy of the
velocity field derived by potential analysis for a fair sample.

The observed CMB fluctuations provide evidence for *initial
fluctuations* (H2), consistent with a scale-invariant *n* ~ 1
spectrum. The observed motions are also consistent with *n* ~ 1
(Section 7.1) (with the uncertain LP
result as a possible exception). The
indications for somewhat higher large-scale power in the clustering of
galaxies (Maddox *et al.*
1990) may reflect non-trivial biasing. The
question of whether the fluctuations were Gaussian (H2) cannot
be answered by observed velocities alone. The PDF
of **·** **v** is
consistent with Gaussian initial fluctuations
skewed by non-linear gravity, but this is not a very discriminatory test.
Nevertheless, the galaxy spatial distribution does indicate Gaussian
initial fluctuations convincingly
(Section 7.2)

Can we tell the nature of the *dark matter* (H3)? In view of the
tight nucleosynthesis constraints on baryonic density, the high
indicated by the motions requires non-baryonic DM. The mass-density
PS on scales 10-100 h^{-1}Mpc is calculable in principle but the
current uncertainties do not allow a clear distinction between the
possibilities of baryonic, cold, hot or mixed DM. The mixed model seems
to score best in view of the overall LSS data, as expected from a model
with more free parameters, but CDM in fact does somewhat better in
fitting the large-scale motions. I do not think that any of the
front-runner models is significantly ruled out at this point, contrary to
occasional premature statements in the literature about the ``death'' of
certain models. I predict that were the DM constituent(s) to be
securely detected in
the lab, the corresponding scenario of LSS would find a way to overcome
the ~ 2 obstacles it is
facing now.

What can we conclude about the *background cosmology* (H1)? All the
observations so far are consistent with large-scale homogeneity and
isotropy (with the exception of the 2 LP discrepancy). The motions
say nothing about *H* or
(Lahav *et al.* 1991), but
they provide a unique opportunity to constrain in several different ways.
Some methods put a strong (> 3) lower bound of
> 0.2-0.3. This is
consistent with the
theoretically-favored =
1 but ``ugly'' values near
0.5 are not ruled out
either. The range of
values
obtained on different scales is partly due to errors, and
any remaining difference may be explained by a scale-dependent non-linear
biasing relation between the different galaxy types and mass.
The data are thus consistent with the predictions of Inflation:
flat geometry and Gaussian, scale-invariant initial fluctuations.
Recall however that = 1
predicts *t*_{0} = 6.3 h^{-1} Gyr, which
will be in conflict with the age constraints from globular clusters,
*t*_{0} = 15 ± 3 Gyr, if the Hubble constant *h*
is not close to 0.5.

The rapid progress in this field guarantees that many of the results and uncertainties discussed above will soon become obsolete, but I hope that the discussion of concepts will be of lasting value, and that the methods discussed can be useful as are and as a basis for improvements.

ACKNOWLEDGMENTS

I thank G. Ganon, T. Kolatt, S. Markoff and I. Zehavi for assistance, M. Hudson and A. Yahil for plots, and G. Blumenthal, S.M. Faber, Y. Hoffman, O. Lahav, M. Strauss, D. Weinberg, J. Willick, and A. Yahil for very helpful comments. This work has been supported by grants from the US-Israel Binational Science Foundation and the Israel Basic Research Foundation.