This paper reviews the present state of the theory of primaeval whirls which may be responsible for the origin of galaxies and galaxy systems. The main problems on which the author will concentrate are concerned with the pre-recombination evolution of the whirls. Special attention is given to new results, obtained by Kurskov and the author, concerning the dissipation of cosmological turbulence and the constraints which follow on the parameters of primaeval whirls. In contrast to some assertions in the literature, there is not contradiction between the whirl concept and observations. Moreover, the fact that the final spectrum of motions and corresponding inhomogeneities does not depend essentially upon the details of the initial whirl spectrum makes the theory very attractive.

The formation of galaxy systems (groups, clusters etc.) is discussed, and alternatives for the formation of galaxies themselves are briefly outlined. Many aspects of the whirl theory are suitable for further observational and theoretical development.

From the standpoint of the turbulent origin of the formation of galaxies, it is important whether the primordial cosmic turbulence can survive up to the necessary epoch against acoustic decay. This is a preliminary report of our new formalism for attacking the problem.

Singularities in space-time can be broadly divided into three classes: past-spacelike (in white holes or the big bang), timelike (naked singularities) and future-spacelike (in black holes or the final recollapse). In a closed Universe, if a simple restriction is made to eliminate timelike singularities, the inference may be drawn that the topology of the Universe is unchanging with time. Thermodynamical considerations lead one to infer that the final singularity of recollapse must differ markedly in structure from the initial big bang. This may plausibly be related to the existence of black holes and the presumed non-existence of white holes.

Observations primarily of the microwave background radiation show that the Universe expands isotropically with a high degree of accuracy at the present time and that the matter distribution is homogeneous on a large scale. Thus, the Friedmann cosmological models are a good approximation today for the expanding Universe. This is valid for at least some period of time in the past too. But how did the Universe expand and what was the matter distribution close to the starting point, near the cosmological singularity?

The most important cosmological observation in the last forty years has undoubtedly been the discovery of the microwave background. As well as confirming the existence of a hot early phase of the Universe, by its spectrum, its remarkable isotropy indicates that the Universe must be very nearly spherically symmetric about us. Because of the revolution of thought brought about by Copernicus, we are no longer vain enough to believe that we occupy any special position in the Universe. We must assume, therefore, that the radiation would appear similarly isotropic in any other place. One can show that the microwave radiation can be exactly isotropic at every point only if the Universe is exactly spatially homogeneous and isotropic, that is to say, it is described by one of the Friedmann models. (Ehlers et al., 1968). Of course, the Universe is neither homogeneous nor isotropic locally. This must mean that the background radiation is not exactly isotropic, but only isotropic to within the very good limits set by the observations (about 0.1%). One would like to know, however, what limits the observations place on the large-scale anisotropies and inhomogeneities of the Universe. One would also like to know why it is that the Universe is so nearly, but not exactly, isotropic.

Prof. Wheeler has asked me to say something for the record about some ideas that I once suggested (at the Clifford Memorial meeting in Princeton in 1970) and to which Hawking and Collins have referred (Astrophys. J.180, 317, 1973). This concerns a line of thought which I believe to be potentially fertile, but which I did not write up at the time because I felt (as I still feel) that it needs further development. However, it is not inappropriate that this matter should have cropped up again on the present occasion, since it consists basically of a reaction against exaggerated subservience to the ‘Copernican principle’.

An intense non-thermal background of cosmic gravitational radiation in the Megaparsec wave band could be detected by its influence on many astrophysical processes. In particular, it may give an explanation of the so-called redshift anomalies.

Inhomogeneous generalizations of the Kasner cosmological models have been found by Gowdy, and can be used to exhibit simplified models of quantized gravitational fields. One finds that a quantum description can be given arbitrarily near the singularity. Graviton pair creation occurs, and can be seen to convert anisotropic expansion rates into the energy of graviton pairs.

The creation of particles is a process which can only be described by quantum field theory. The old classical theories dealing with indestructible particles are incompatible with particle creation. It was the discovery of the corpuscular nature of light (Einstein, 1905) and the prediction of antiparticles (Dirac, 1929) which demonstrated that particle creation was possible. The creation of particles may influence the cosmological equations through the energy-stress tensor of these particles. For physical cosmology the particles themselves are important. Therefore this report deals with a particular example of the impact of quantum mechanics on cosmological theory.

In a big bang cosmology in which the Universe is initially filled with thermal radiation at a very high temperature the number of nucleon-antinucleon pairs decreases exponentially with temperature when the latter falls below a value such that kT ~ 1 GeV. To explain the observed ratio η = N/Nph ~ 10-9 where N is the average baryon density and Nph the photon density, nucleons and antinucleons must have been separated in the thermal radiation at a temperature greater than 30 MeV. A mechanism has been suggested which would lead to a phase transition in thermal radiation for kT > 300 MeV resulting in two phases with opposite non zero baryon number. The interaction between nucleons and antinucleons at intermediate energy is repulsive according to the mesonic theory of nuclear forces. This can be checked experimentally by measuring with enough precision the energy of X-rays emitted by the protonium atom and this experiment is now under way at CERN. Different models have been made to investigate their consequences and in each case a phase transition has been found above a temperature of the order of 300 MeV (Omnes, 1972; Aldrovandi and Caser, 1973; Cisneros, 1973).

Most cosmological models are based on the ‘cosmological principle’ according to which the Universe is homogeneous and isotropic on a certain level, chosen such that the present mean density is of the order of 10-30±1 g cm-3.

The presence of large amounts of antimatter in the Universe would be detectable directly via the cosmic rays and indirectly via the annihilation γ-rays. The observational data is reviewed. There is no evidence whatever indicating the presence of astrophysically interesting amounts of antimatter in the Universe. From the available data we may conclude that the Galaxy is made entirely of ordinary matter and that if any antimatter at all is present in the Universe, it must be very well separated from ordinary matter. Furthermore, we show that the observational constraints on various symmetrical cosmological models strengthen the case against antimatter in the Universe.