When protogalaxies collapse, the cooling and infall of what will become the visible galactic component affects the mass distribution of dissipationless dark matter particles which constitute the halo. For spiral galaxies, the reaction of the dissipationless halo can have a striking effect on the resulting rotation curves [1–5].

A universe dominated by both hot (HDM) and cold dark matter (CDM) is proposed. In this context, the new features for the formation of dwarf galaxies, Lyα clouds, galaxies, and large-scale structures are presented.

Cosmological arguments suggest that a large fraction of the baryons in the Universe are dark. Although the background dark matter required to make up the critical density would have to consist of some kind of elementary particle, the dark matter in galactic halos could be baryonic. In particular, we argue that it could consist of jupiters made in pregalactic or protogalactic cooling flows. These would be analagous to the cluster cooling flows observed at the present epoch but on a smaller scale.

The clustering properties of galaxies are incompatible with a cosmological model with Ω = 1 unless the formation process for bright galaxies is ‘biased’ in the sense that their resultant distribution exaggerates the amplitude of large-scale inhomogeneities in the overall mass distribution. The mechanisms for such biasing are intimately connected with the nature of the dark matter. Various possibilities are summarised here.

The gravitational lensing phenomenon is a new observational tool in cosmology. It appears to occur reasonably frequently; several thousand examples probably are observable with current radio and optical telescopes. A dozen or so reasonable candidates have been proposed, but it has become clear that one must apply strong tests to distinguish between real examples of lensing and chance associations. The dramatic double quasar 1146+111 has emphasized the need to be rigorous, and data is presented that casts further doubt on its status as a lens. There are a number of well-established cases, however, and these illustrate the varied character of possible lenses. Present observational programs should enlarge the number of established examples. Time-delay measurements are also in progress that give a new class of cosmological test; the original lensed quasar pair 0957+561 seems to have a differential time delay provisionally estimated at 600 ± 200 days for the two principal images.

A gravitational lensing model is proposed to explain the giant arc structure we observed in September 1985 in the distant cluster of galaxies Abell 370 (z=0.37.4).

During a program of study of surface brightness of elliptical galaxies in large redshift clusters in 1976 by a video camera at the KPNO 4-meter telescope, we in colaboration with Alan Sandage discovered filamentary and arc-like features in three clusters of galaxies. More recently, the same clusters (Abell 370, Abell 2218, and Cl2244-02) were observed by three different CCD's at the same telescope. These new observations confirm ouir old observations, and being of higher quality, show that the features in two of the clusters (Abell 370 and Cl 2244) form well defined continuous arcs with the following properties:

1. 1) Large nearly circular features (length and radius of curvature ∼100 Kpc) with the center of curvature located near the center of gravity of the cluster.

2. 2) Large optical luminosity (≃1011L⊙).

3. 3) Bluer than the elliptical galaxies with unexpectedly high ultraviolet emission for Abell 370 giving rise to an unusual spectrum (see figure 1).

4. 4) Nearly uniform width along the arc with almost abrupt termination points, indicating a one dimensional structure rather than projection of a portion of a spherical shell.

5. 5) the arcs are nearly resolved perpendicular to their length with widths of ≤ 1″ (≤ 6 Kpc).

   1. i) In case of Abell 370 the surface brightness is very uniform but the width varies with wavelength, becoming wider toward blue and ultraviolet.

   2. ii) In case of CI 2244 there is considerable variation of surface brightness along the arc. We have no information on the variation of the width with wavelength.

6. 6) Our data does not show any other unusual features associated with the clusters as a whole or with the giant cD galaxies. These clusters may, however, be unusual in that they seem to have two distinct centers of gravity, this is especially true for Abell 370 which has two almost identical giant cD galaxies instead of the usual clusters dominated by one centrally located cD galaxy.

7. 7) Polarization observations show that the arcs are not highly polarized (polarization < 20%).

8. 8) From a short exposure spectral observation of C12244 we can only deduce absence of very strong emission lines.

A brief review is given on the present status of the “fifth force”, followed by the study of its cosmological consequences. If the force is indeed mediated by a massive vector field, we expect a period t ≲ 10−13 sec in which the universe cooled down like T ∼ t−1.

This conference has been marked by our willingness to entertain grand schemes of synthesis of theoretical ideas and the observational evidence on how galaxies and large-scale structure might have formed. At IAU Symposium 104 on this subject held in Crete just 5 years ago there was little discussion of how all the pieces of the puzzle might fit together. Now we have at least three candidate grand syntheses that have been worked out in some detail and have been discussed here: scale-invariant cold dark matter, by Frenk; massive cosmic strings, by Turok; and exploding magnetized superconducting cosmic strings, by Ostriker. I have accordingly placed each of the topics I want to review under the heading of the grand scheme for which it seems most embarrassing. This negative approach is a little unfair, but I think we can take it as given that we would not be considering a scheme that did not have many good points, and that the real interest is the probing of weak points by which we hope to learn which schemes might be strengthened, which might safely be abandoned.

Recently Nagoya-Berkeley group (Matsumoto et al, 1987) observed microwave radiation in the Wien region precisely and found the excess of temperature. In the previous paper (kawasaki and Sato, 1986), we investigated the distortion of the spectrum of microwave background radiation due to the radiative decay of weakly interacting massive particles. At that time, however, the distortion was not observed. In the present paper, we investigated in detail whether the decay of WIMPs can account for the observed distortion of the spectrum or not. In Fig. 1, an example is shown.

The Shane & Wirtanen (SW) galaxy catalog, as reduced by Seldner et al (SSGP), is used to calculate the dipole vector of the galaxy distribution. The catalogue covers 86% of the North and 53% of the South Galactic cap (totally 8.8 steradians) and contains about 810,000 galaxies binned in 10′ × 10′ cells with magnitude limit mB ∼ 18.8. Dipoles have been found in the IRAS and in an optical catalogue based on the ESO, UGC and MCG catalogues, with average depths of ∼ 100 h−1 and ∼ 50 h−1 Mpc respectively. The direction of these dipoles is consistent with that of the microwave background dipole which means that the structures responsible for the dipole are present within the limits of the shallower catalogue and dominate the large-scale morpology of the galaxy distribution in both catalogues. It can therefore be expected that these structures will be ‘washed out’ by more distant structures dominating the deeper SW catalogue. The characteristic depth of the SW catalogue is 360 h−1 and the median depth of a cluster sample, identified from the SW catalogue by an objective proccedure, is ∼ 180 h−1 Mpc. Even if a dipole is found there is no apparent reason for it to point towards the MWB dipole direction since other galaxy fluctuations, comparable in size with those responsible for the MWB dipole, should be present in the SW catalogue if the Cosmological Principle is relevant on scales traced by the catalogue.

On large scales where linear perturbation theory is valid, the mean square values of the mass excess , the peculiar velocity ν and the microwave background anisotropy due to the Sachs-Wolfe effect, are simply expressed in terms of the present-day power spectrum of the density irregularity P(k):

We have calculated the anisotropies of the cosmic microwave background radiation in a baryon-dominated model (BDM), using a gauge invariant method. The results on a 4.5′ angular scale are as follows (h = 0.5 and initially Zel'dovich power spectrum assumed):

Density fluctuations needed for galaxy formation may have thermal origin in a tepid inflation.

Talcing into account vacuum polarization effects and a coherent massive scalar field we consider a singularity free cosmological model from which an intermediate inflationary stage follows quite naturally. According to the ideas of Tryon, Fomin, Zeldovich and others on the spontaneous creation of an universe by a quantum process the newly created universe must be closed. Its evolution starts from a finite initial value a of the order of the Planck length with a zero velocity ho = 0 (h - Hubble parameter). Therefore, in this moment an effective source term not fulfilling the strong energy condition must be dominant. It can originate fron a coherent massive scalar field (mass m) with zero kinetic energy and/or the vacuum polarization (considered here in the form of a modified gravitational Lagrangian with quadratic terms of the Ricci scalar). The corresponding general Lagrangian reads (c = h =1) where ∝ is a negative coupling constant and Lmat is the Lagrangian of other possible existing matter. Both the massive scalar field and the vacuum polarization effects drive the universe to expand exponentially for a definite time interval depending on the initial radius a0 and the parameters m and ∝, during which all other matter being originally present is diluted. The following small oscillations superimposed on the dust-like power law behaviour of the scale factor cause an intensive particle production, and the universe heats up to a radiation dominated Friedmann universe. This process must terminate before baryogenesis. The matching of the different phases of the cosmological evolution and the requirement to fit the parameters of the observed universe lead to a definite parameter range for m and |∝| well below the Planck values. In consequence the present mass density must be equal to the critical one (Ω = 1) with high accuracy.

The presence of the cosmical constant introduces a fundamental scale and prevents there being any simple self-symmetry. Henriksen, Emslie and Wesson (HEW), who studied spherically-symmetric models with a positive cosmical constant, have, however, demonstrated the possible existence of a self-similarity of the second kind and identified the similarity variable. They obtained interesting analytic solutions which are homogeneous in density, but not in pressure. We have extended this work and investigated the general behaviour of these cosmological models which possess a self-similarity of the second kind and in which the requirement of homogeneity is relaxed.

It is the purpose of this paper to illustrate the interrelation between the problems of the “missing mass”, the galactic age and the cosmological constant Λ (or its equivalent quantum vacuum density ).

It is shown that the solutions for the non-linear equations governing the motion of a stratified self-gravitating isothermal fluid are generated by a sine-Gordon equation (SG) which has well-known soliton solutions. Starting with two solutions of the SG-equation which are related via an auto-Baecklund-transformation, the physical quantities, density, velocity and gravitational potential are expressed in a parametric form in terms of characteristic coordinates. The zero-solution and the one-soliton solution of SG generate a single hump in the density moving with constant velocity. The typical non-linear feature is the relation between amplitude A and width (y = square of the speed of sound). The 1-soliton together with the 2-sollton solution of SG produces two moving humps in the density which come to rest asymptotically. As a result of the interaction the ratio amplitude/width is different from the corresponding ratio of the single soliton. Due to a certain exchange symmetry in the transformation procedure relating the SG to the gravity system it is possible to generate another solution out of the 2-soliton. Which represents a single hump moving on a homogeneous background. The remarkable property is that the density becomes infinite in a finite time depending on the amplitude. The “breather”-solutlon of SG produces a density distribution that represents two pulses colliding onto a central hump at rest which are separated from each other by a discontinuity in the density and the velocity field. These solutions may have applications to the non-linear evolution of flat structures arising in the process of galaxy formation.

We compare the luminosity function and the two-point spatial correlation function for the two slices of the CfA redshift survey extension to mB(0) ≤ 15.5 [8h ≤ RA. ≤ 17h and 26.5° ≤ DEC. ≤ 38.5°], with those for the early survey limited to mB(0) ≤ 14.5 [bII ≥ 40°, and DEC. ≥ 0°]. The derived properties of the two samples agree within the errors. The parameters of the luminosity function are M* = −19.1±0.1 and α = −1.2±0.1 for the 15.5 sample, and M* = −19.3±0.1 and α = −1.1 ± 0.1 for the 14.5 sample. We use an inhomogeneity-independent method to calculate the luminosity function. The slopes of the correlation functions for the two samples are −1.5 ± 0.35, shallower than the canonical slope of −1.8. The correlation lengths are 7.5 ± 5h−1 Mpc, larger than the correlation length of 5h−1 Mpc matched to the theoretical models. Because of the 25% uncertainty in the mean density of the 15.5 sample, the correlation function is indeterminate on scales larger than ∼ 20h−1 Mpc.