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

9. DISCUSSION: ARE THE HYPOTHESES JUSTIFIED?

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^-1Mpc (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^-1Mpc 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^-1Mpc-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^-1Mpc. 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^-1Mpc 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 t₀ = 6.3 h^-1 Gyr, which will be in conflict with the age constraints from globular clusters, t₀ = 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.