We have generalized the classical description of ionization front propagation to the case of a point source in a uniform, cosmologically expanding gas. We present illustrative curves for the comoving radius and peculiar velocity for several turn-on redshifts, z0N, for Ωtot = 1, Ωb = 0.1, h = 1. The quantity RS is the generalized Strömgren radius [RS = RSi (1 + z0N)/(1 + z), RSi = (3Nu/4πnH,i2 α2)1/3, Nu = photoionizing number flux per source, α2 = recombination rate to n = 2, nH,i = nHo (1 + z0N)3]. The quantity T0N = 2 (1 + z0N)−3/2/(3H0). We also plot ζ, the value of (2nQoNph, Q/3HonHo) needed to ionize the IGM with overlapping QSO HII regions by redshift z0V for QSO turn-on at various z0N, where Nph, Q = ionizing photon luminosity per QSO, nQo = QSO number density (present co-moving value), nH = H density of IGM, and nH/nHo = nQ/nQo = (1 + z)3. From a recent preprint by Koo (1985), we estimate ζ ≲ 1 (for Ωb = 0.1, h = 1) for QSO's with L ∼ 1045 erg s−1. In this case, the observed QSO's cannot be the sole source of the IGM ionization that is implied by the null detection of the Gunn-Peterson effect for QSO's with z > 2.

We present a simple model for the formation of elliptical galaxies, based on a binary clustering hierarchy of dark matter, the chemical enrichment of the gas at each level being controlled by supernovae. The initial conditions for the non-linear phases of galaxy formation are set by the post-recombination power spectrum of density fluctuations. We investigate two models for this power spectrum - the first is a straightforward power law, |δk|2 ∝ kn, and the second is Peeble's analytic approximation to the emergent spectrum in a universe dominated by cold dark matter. The normalisation is chosen such that on some scale, say M ∼ 1012M⊙, the objects that condense out have properties - radius and velocity dispersion - resembling ‘typical’ galaxies. There is some ambiguity in this due to the poorly determined mass-to-light ratio of a typical elliptical galaxy — we look at two normalisations, σ1D ∼ 350kms−1 and σ1D ∼ 140kms−1. The choice determines which of Compton cooling or hydrogen cooling is more important during the galaxy formation period. The non-linear behaviour of the perturbations is treated by the homogeneous sphere approximation.

The astronomical data show that most of the mass in the Universe is dark. At present there are a few models of the dark matter: (i) the standard neutrino model, (ii) the model with unstable neutrinos, (iii) axion model. All models can be modified with Λ - term which plays role of the homogeneous component of the dark matter. In this paper the non-linear processes of gravitational instability are briefly discussed.

Both large and small-scale ΔT/T anisotropies of the microwave background are reviewed in the context of the modern theories of the Universe structure origin. A number of primordial perturbation spectra and various types of cosmological missing mass are considered. Theoretical predictions are compared with the observational data. Importance of the ΔT/T measurements on large angular scales (θ > 5°) is emphasized.

Following the standard scenario of galaxy formation, density fluctuations with amplitude δ∼10−3 should have been present at the recombination time tR in order that galaxies and clusters of galaxies can be formed. Recent observations of the anisotropy of the cosmic background radiation(CBR), however, indicate that δ is less than 10−4 at tR for adiabatic perturbations in the baryon-dominated universe.

There still seem to be three serious contenders for the dark matter in galactic halos and groups of galaxies: (i) very low mass stars, (ii) black hole remnants of very massive stars or (iii) some species of particle (e.g. axions, photinos, etc.) surviving from the big bang. There are genuine prospects of detecting individual objects in all three of these categories, and thereby narrowing down the present range of options. If the Universe has the critical density (Ω = 1), rather than the lower value (Ω = 0.1–0.2) inferred from dynamical evidence, then the galaxies must be more clustered than the overall distribution even on scales 10–20 Mpc. “Biased” galaxy formation could account for this.

There is evidence for four types of dark matter: (1) the local d.m. in the galactic disc; (2) the d.m. associated with galactic halos; (3) the d.m. in clusters; and (4) a background closure density of d.m. required if the Universe undergoes an inflationary phase. There are three types of explanation: (1) remnants of a first generation of Population III stars, including black holes (SMOs, VMOs or MOs), neutron stars, white dwarfs, or LMOs (M-dwarfs and Jupiters); (2) elementary particle relicts of the Big Bang (inos), usefully classified - according to their mass - as hot, warm, or cold, since this determines the scale on which they can cluster; and (3) primordial black holes, formed from density perturbations or phase transitions in the early Universe. Various constraints on the d.m. candidates are indicated by the shaded regions in the Figure below. The conventional model of cosmological nucleosynthesis precludes Population III remnants providing the closure and perhaps cluster d.m., while stellar nucleosynthesis constraints preclude neutron stars from explaining anything and allow white dwarfs to provide only the local d.m. Source counts exclude M-dwarfs from providing the local or halo d.m., while gravitational lensing effects exclude SMOs larger than 108M⊙ from explaining anything and LMOs or VMOs from having the closure density. Dynamical considerations imply M<2M⊙ for the local d.m., M<106M⊙ for the halo d.m., and M<109M⊙ for the cluster d.m.; they also imply that the local d.m. cannot be inos and that the halo d.m. cannot be a hot ino. The table suggests the following conclusions: (1) no single candidate can explain all four d.m. problems; (2) the best candidate for the closure d.m. is an ino; (3) the best candidates for the local d.m. are white dwarfs or Jupiters; (4) the halo (and possibly cluster) d.m. could plausibly be black holes or Jupiters.

A set of comprehensive computer models for the chemical evolution of galaxies have been used to determine the limits on the amount of mass that could exist in the form of dark stellar remnants deriving from normal stellar evolutionary processes. In these models, the instantaneous recycling approximation is not assumed: stars are binned into 10 mass intervals, with different lifetimes, yields and remnant masses. The models were run using many different values for the IMF (including non-Salpeter and varying IMFs), star formation rates, yields, remnant masses, gas infall and outflow rates, primordial metalliciy and initial conditions. The Galaxy is described by a two-zone halo-disk system, where gas from the halo falls onto the disk. Elliptical galaxies are described by single-zone models.

We consider the idea that galaxy halos are composed of massive black holes, as a possible resolution of two problems: the composition of dark halos, and the heating of stellar disks. Scattering of disk stars by halo black holes with mass MH, velocity dispersion σH and number density nH causes the stellar velocity dispersion to increase with time t as σ≈(Dt)1/2 for t large, where D α nHM2H in Λ/σH, and in Λ is the Coulomb logarithm. This time-dependence is in good agreement with observations, as is the prediction for the axial ratios of the velocity ellipsoid σu: σv: σw. To account for the magnitude of the disk velocity dispersion in the solar neighbourhood, we require MH≈2 × 106M⊙. The stellar distribution function is predicted to be approximately isothermal at low epicyclic energies, in the Fokker-Planck regime in which the effect of the many distant, weak encounters dominates, but with a power-law tail at high energies produced by the relatively rare close encounters. This tail has the form N(E)αE−2, where E is the horizontal or vertical epicyclic energy, and N(E) is the number of stars per unit area of the disk, per unit E. The fraction of stars in this power-law tail depends only on the value of in Λ, and is about 1% for typical values. This provides a possible explanation for the high velocity A stars found in the solar neighbourhood. This disk heating mechanism can also account for the approximate constancy of the disk scaleheight with radius that is observed in other spiral galaxies, although this does not result as naturally as the other properties.

Current data on the luminosity function of nearby stars allow the possibility that the stellar initial mass function (IMF) is double-peaked and that the star formation rate (SFR) has decreased substantially with time. It is then possible to account for all of the unseen mass in the solar vicinity as stellar remnants. A model for the solar neighborhood has been constructed in which the IMF is bimodal, the SFR is constant for the low-mass mode and strongly decreasing for the high-mass mode, and the mass in remnants is equal to the column density of unseen matter; this model is found to be consistent with all of the available constraints on the evolution and stellar content of the solar neighborhood. In particular, the observed chemical evolution is satisfactorily reproduced without infall. The total SFR in the model decreases roughly with the 1.4 power of the gas content, which is more plausible than the nearly constant SFR required by models with a monotonic IMF.

It has been proposed (e.g. Carr, Bond and Arnett 1984) that the first generation of stars may have been Very Massive Objects (VMOs, of mass above 200 M⊙) which existed at large redshifts and left a large fraction of the mass of the universe in black hole remnants which now provide the dynamical ‘dark matter’. The radiation from these stars would be present today as extragalactic background light. For stars with density parameter Ω* which convert a fraction ϵ of their rest-mass to radiation at a redshift of z, the energy density of background radiation in units of the critical density is ΩR = εΩ* / (1+z). The VMOs would be far-ultraviolet sources with effective temperatures of 105 K. If the radiation is not absorbed, the constraints provided by measurements of background radiation imply (for H =50 km/s/Mpc) that the stars cannot close the universe unless they formed at a redshift of 40 or more. To provide the dark matter (of one-tenth closure density) the optical limits imply that they must have existed at redshifts above 25.

A review of observational searches reveals the following constraints for the constituents of dark halos: (1) Optical searches show that these halos are not for a large fraction of their mass made up of dwarfs of spectral type M5 or earlier. (2) K-band (2.2 μ) searches virtually rule out all H- burning Main Sequence stars. (3) IRAS upper limits are consistent with black dwarfs of any age or Jupiters. (4) The inferred metallicity and M/L variations in the spheroid of NGC 7814 are consistent with the hypothesis that the dark matter consists of low mass objects that formed along with the luminous population II.

Upper limits have been set to the luminosity from the massive halos of three late-type edge-on spiral galaxies: NGC 2683 (Sb), NGC 4244 (Scd), and NGC 5907 (Sc). The limits resulted from simultaneous photometry in the visual (V) and 2.2μm (K) photometric bands which is sensitive to both luminosity and color changes along the minor axes of the three galaxies. The 3σ lower limits to the mass-to-light ratios for the halo of NGC 5907 are the largest ever recorded: M/Lv > 2000 and M/Lk > 64 in solar units. Since K band M/L for M-dwarf stars lying just above the hydrogen-burning limit is about 35, the results virtually eliminate the possibility that hydrogen-burning stars comprise more than a fraction of the halo masses. If the halos contain a more realistic spectrum of stellar masses, for example Population II, the visual band measurements imply that these stars account for less than one percent of the halo mass. Similar limits were obtained for NGC 4244 and NGC 2683. Variations of the V-K colors along and perpendicular to the disks show no sign of population changes toward redder objects at large galactocentric radii.

Preliminary results from a systematic search for nearby substellar objects in the IRAS data bases has revealed only a single candidate among the 12 μm sources in the region of the polar caps. This object appears to be a distant carbon star. All 5700 sources were positionally associated with stars or galaxies.

IRAS 60μ sources are used to map the local (≲200h−1 Mpc, Ho =100h km s−1 Mpc−1) gravitational field, and to determine its dipole component, on the assumption that the infrared radiation traces the matter. The dipole moment is found to point in the direction of the anisotropy of the microwave background radiation. Comparison of the two anisotropies, using linear perturbation theory, yields an estimate of the cosmological density parameter, Ω =0.85±0.16, with nonlinear effects increasing Ωo by ∼15%. The quadrupolar tidal field within the Local Supercluster, due presumably to the same density inhomogeneities, is detected in a kinematical study of the velocity field.

Recent developments in elementary particle physics have led to a renaissance in cosmology, in general, and in the study of structure formation, in particular. Already, the study of the very early (t ≤ 10−2 sec) history of the Universe has provided valuable hints as to the ‘initial data’ for the structure formation problem — the nature and origin of the primeval density inhomogeneities, the quantity and composition of matter in the Universe today, and numerous candidates for the constituents of the ubiquitious dark matter. I review the multitude of WIMP candidates for the dark matter provided by modern particle physics theories, putting them into context by briefly discussing the theories which predict them. I also review their various birth sites and birth processes in the early Universe. At present the most promising candidates seem to be a 30 or so eV neutrino, a few GeV photino, or the ‘invisible axion’ (weighing in at about 10−5 eV!), with a planck mass monopole, quark nuggets, and shadow matter as the leading ‘dark’ horse candidates. I also mention some very exotic possibilities — unstable WIMPs, cosmic strings, and even the possibility of a relic cosmological term.

A new candidate for the dark matter of the universe is strange matter. This substance consists of roughly equal numbers of up, down and strange quarks confined in a quark phase which is conjectured to have a lower energy per baryon number than ordinary nuclei. Strange matter is absolutely stable, has a density comparable to that of nuclei and can exist in lumps ranging in size from a few fermis to ∼ 10 km. If it is distributed in space in lumps larger than ∼ 1 cm, it could close the universe without ever encountering the earth and would be astronomically unobservable.

We consider the use of superheated superconducting colloids as detectors of weakly interacting galactic halo candidate particles (e.g. photinos, massive neutrinos, and scalar neutrinos). These low temperature detectors are sensitive to the deposition of a few hundreds of eV's. The recoil of a dark matter particle off of a superheated superconducting grain in the detector causes the grain to make a transition to the normal state. Their low energy threshold makes this class of detectors ideal for detecting massive weakly interacting halo particles.

We discuss realistic models for the detector and for the galactic halo. We show that the expected count rate (≈103 count/day for scalar and massive neutrinos) exceeds the expected background by several orders of magnitude. For photinos, we expect ≈1 count/day, more than 100 times the predicted background rate. We find that if the detector temperature is maintained at 50 mK and the system noise is reduced below 5 × 10−4 flux quanta, particles with mass as low as 2 GeV can be detected. We show that the earth's motion around the Sun can produce a significant annual modulation in the signal.

On the basis of general properties of the large-scale structure of spacetime, we present new and general theoretical upper limits on the density of dark matter in the Universe, assuming a 90% content for the dark matter, and lower limits on the mass of the axion, assuming the dark matter to be made up of axions. These limits are derived in terms of the possible lower limits to the age of the Universe and the Hubble parameter. We find that for the age in the range (8–24) × 109yr, the maximum density of dark matter is in the range (1.25 × 10−28 −1.38 × 10−29) g cm−3 and the minimum value of axion mass in the ranges (0.36–2.39) × 10−5 eV and (1.44–9.51) × 10−5 eV.

As is known well, the inflationary universe model resolves most of the fundamental problems concerning the large scale structure of the universe and is now becoming a standard model for the early universe. However, there is one important problem yet to be made clear. In this model the number density of particles effectively goes to zero during the inflation and everything is created after the universe is heated up again at the end of inflation. Since the reheating temperature is much lower than the GUT temperature in general, however, it is not clear whether the observed baryon asymmetry is generated in this process.