In a recent paper Simpson has reported evidence for a heavy neutrino of about 17.1 kev mass. Cosmological bounds on stable neutrino species imply that this neutrino [νH] must be unstable. The most likely decay mode νH→νL+f where νL is a light neutrino and f is a scalar boson leads to a cosmological scenario which is quite different from the conventional picture. In this scenario universe becomes matter dominated at a redshift of z ∼ 107 and becomes radiation dominated [by the decay product νL of νH] at z ∼ 310. The kinematic constraints on the lifetime of νH do not lead to any contradictions. On the other hand, growth of baryonic perturbations is severely limited in this model due to two reasons: (i) virtually no growth can take place in the radiation dominated region z ≤ 310. (ii) Decay of νH is likely to disrupt and smoothen out past growth by a large factor. It is doubtful whether a simple way out of this difficulty exists.

Axions are a natural consequence of the only known solution of the ‘Strong CP Problem.’ The axion represents a minimal U(1) extension to the standard SU(3) × SU(2) × U(1) model of the strong and electroweak interactions and furthermore appears very frequently in the contexts of SUSY GUTs, Kaluza-Klein, Superstring, Technicolor, and other unified models. As such, the axion is perhaps the best motivated conjectured particle.

If the halo of our galaxy is composed of weakly interacting particles, they will be captured by the sun. If the mass of these particles exceed 5 proton masses, they will remain in the Sun where they will serve as an effective means of transporting energy in the solar core. They will make the Sun's core more nearly isothermal, thus decreasing the rate of the PPIII reaction. If the halo is composed of particles with masses between 5 and 10 GeV and cross section between 10−34 and 10−37 cm2, this mechanism could resolve the solar neutrino problem. If these particles exist, they could be detected by a low temperature detector. However, if the particles annihilate in the Sun, (e.g. Photinos or Scalar Neutrinos), their number density will be too low.

Recently cosmology with unstable particles has attracted much attention as a possible solution to several important problems in the present universe. In this scenario, however, nonlinear structures in the universe would not easily form since their binding energy would decrease gradually in the course of the decay of unstable particles. Thus this scenario is stringently constrained by the galaxy formation problem. In order to obtain the constraints quantitatively, we carried out numerical calculations of the evolution of density perturbations after the time of recombination. Universe is assumed to consist of three components; unstable X-particles, its non-radiative decay product (massless particles) and baryons. Initial conditions are specified by the density contrast of X-particles δX,i and the baryon density parameter Ωb,i. Resultant baryon density contrast at Z = 4 (epoch of galaxy formation) and Z = 0 (present) is shown below for Ωb,i = 0.005.

A possibility of a universe dominated by unstable particles has been suggested recently as an interesting solution to various cosmological problems. In this scenario, however, nonlinear structures may be disrupted or even smoothed out during the decay of unstable particles. In order to obtain the survival condition of baryon structures, we studied evolution of systems composed of baryon and unstable particles by the numerical integration of the Vlasov equation.

Primordial nucleosynthesis which is responsible for the formation of the lightest elements (D, 3He, 4He and 7Li) provides a unique way to determine the present baryon density pB in the Universe and therefore the corresponding cosmological parameter ΩB. After a brief summary of the relevant abundance determinations and of the consequences of the Standard Big Bang nucleosynthesis, it is argued that one needs to call for specific models of chemical evolution of the Galaxy in order to reconcile the observations with the predictions of this model. In this context the predicted values for ΩB should range from 4 10−3 to 6 10−2. These values are significantly lower than those deduced from current M/L determinations.

I will attempt in this talk to address the questions that Drs. Schwarzschild and Faber posed at the beginning, in the light of what has been said in the last few days and a few things that were not but perhaps should have been.

The dominant impression which I carry away from this meeting is that extragalactic astronomy has reached a crisis (‘a state of affairs in which a decisive change for better or worse is imminent’, according to Fowler). The nature, origin and distribution of the dark matter and its role in galaxy formation and dynamics are issues whose resolution is likely to determine the direction of studies in galactic structure and cosmology for decades to come.