I have been invited by the organisers to provide an overall perspective on the subject of this Symposium. Necessarily, this will be a subjective impression of topics in which there has been quite remarkable progress since the last General Assembly of the IAU, and which are of the greatest interest for the whole of science. In preparing a review of such an enormous field, one veers between optimism and pessimism about the successes and problems which have arisen. I hope to steer a realistic course between these extremes. Fortunately, there are many experts participating in this Symposium who will be able to neutralise my personal biases and provide authoritative opinions on all the topics I will cover.

A Joint Discussion on the extragalactic distance scale and the Hubble constant took place fifteen years ago, at the 1982 XVIIIth General Assembly of the IAU, held in Patras, Greece. At that time, the newest applications of infrared photometers to Tully-Fisher measurements (Aaronson 1983) and Cepheid distances (Madore 1983) were reported. CCDs were just coming into use and had not yet been applied to extragalactic distance determinations; all of the extragalactic Cepheid distances were based on photographic Argelander (eye-estimated) photometry (Tammann and Sandage 1983 and references therein). No Cepheid distances to type Ia supernova-host galaxies were available.

A linearity test shows H0 to decrease by 7% out to 18 000 km s–1. The value at 10 000 km s–1 is a good approximation to the mean value of H0 over very large scales. The construction of the extragalactic distance scale is discussed. Field galaxies, cluster distances relative to Virgo, and blue supernovae of type Ia yield H0 (cosmic) with increasing weight; they give consistently H0 = 57 ± 7 (external error). This value is supported by purely physical distance determinations (SZ effect, gravitational lenses, MWB fluctuations). Arguments for H0 > 70 are discussed and shown to be flawed.

The period–luminosity (PL) relation of the Cepheid variable stars is the most reliable primary distance indicator for nearby galaxies, and serves as the foundation of the extragalactic distance scale, providing the firm calibration for various secondary distance indicators. However, a major disadvantage of the Cepheid distance scale is that it can only be applied to late–type systems with recent or current star formation. An alternative distance indicator is a Pop II, tip of the red giant branch (TRGB) method, which is extremely attractive because of its applicability to all morphological types of galaxies. As long as a metal–poor RGB stars are present in abundant numbers, the distance can be estimated with an accuracy that is as good as that of the Cepheid PL relation.

The first section discusses a recalibration of the luminosity–linewidth technique and its use in a determination of H0. The recalibration introduces (i) new cluster calibration data, (ii) new corrections for reddening as a function of inclination, and (iii) a new zero-point calibration using 13 galaxies with distances determined via the cepheid period–luminosity method. It is found that H0 = 82 ± 16 km s−1 Mpc−1 (95% confidence).

We present new calculations of the gravitational lensing statistics following recent revised knowledge of the luminosity function and internal velocity dispersion of E/S0 galaxies which work as effective lenses for background high-redshift QSOs. We show that the theoretical prediction of the lensing statistics is much smaller than previously expected. In sharp contrast with the earlier statistics supporting an Ω0 = 1 universe, the reported small lensing probability from the Hubble Space Telescope (HST) snapshot lens survey is in best agreement with a low-density, flat universe with Ω0 ≃ 0.2 and Ω0 + λ0 = 1. The age of this universe, combined with the HST measurement of a high value of the Hubble constant H0, can be reconciled with the age of the oldest globular clusters in the Milky Way (ApJ, 1997, Vol. 489, in press).

ASCA, Japanese X-ray Sattelite, can obtain the spatial distribution of density and temperature of the intracluster medium at the same time and greatly improve the accuracy for the derivation of the Hubble constant using the thermal Sunyaev-Zel'dovich effect. Table 1 shows the results of ASCA observations of 4 distant clusters of galaxies. The parameters of the density distribution were obtained assuming the β model.

Very Long Baseline Interferometry (VLBI) allows us to study a core of AGN with a sub-parsec resolution. We analyze the dependencies “apparent angular size – redshift” and “apparent motion – redshift” which contain an imprint of the source's properties and cosmology. We present data on the “angular size – redshift” relation obtained with VLBI at 5 GHz on a sample of 300 AGN distributed over the widest available range of redshifts 0.016 ≤ z ≤ 4.5. The sample exceeds those used in similar studies earlier by Kellermann (1993, 79 sources) and Wilkinson et al. (1997, 160 sources). Unlike extended source, the angular size-redshift for compact radio sources appears consistent with the predictions of standard Friedmann world models with qo ≃ 0.5 without taking into account evolutionary effects or selection effects due to a “linear size – luminosity” or “linear size – spectral index” dependences. We discuss different approaches allowing us to disentangle intrinsic evolutionary properties of sources and parameters of the cosmological model. Recent estimates of parameters of the cosmological model are given. We also discuss a perspective of conclusive cosmological tests using the VLBI technique.

The large luminosity (MV ≈ −19 ∼ −20) and the homogeneity in light curves and spectra of Type Ia supernovae(SNe Ia) have led to their use as distance indicators ultimately to determine the Hubble constant (H0). However, an increasing number of the observed samples from intermediate- and high-z (z ∼ 0.1 − 1) SN Ia survey projects(Hamuy et al. 1996, Perlmutter et al. 1997) have shown that there is a significant dispersion in the maximum brightness (∼ 0.4 mag) and the brighter-slower correlation between the brightness and the postmaximum decline rate, which was first pointed out by Phillips(1993). By taking the correlation into account, Hamuy et al.(1996) gave an estimate of H0 within the error bars half as much as previous ones.

The new Hipparcos parallax data for local subdwarfs allow a much more reliable determination of the distance to globular clusters (by direct sequence fitting) than was previously possible. Earlier studies (Reid 1997, Gratton et al. 1997) have reported larger distances than expected, especially for the most metal-poor clusters, implying much younger ages. In our study of Hipparcos subdwarfs applied to M92 — representative of the oldest, most metal-poor clusters — we find however a distance only slightly in excess of previous expectations. We show, using Monte Carlo simulations, that most of the difference may be explained by our more detailed treatment of the Lutz-Kelker and selection biases. With up-to-date stellar evolution models, we derive a minimum age of 13 Gyr for the Universe. This value, although lower than previous estimates, still imposes a rather strict upper limit to Ho in the context of standard cosmological models.

The accuracy of measurement of the Hubble constant depends not only on the accuracy of distance measurement but also on how small is the effect of local flows: The larger are redshifts of used galaxies, the higher is the accuracy of H0, if the error in distance measurement is comparable. The HI Tully-Fisher relation has been the standard tool for distance measurement up to cz ∼ 10,000 km s–1 (Tully and Fisher 1977), where, however, the local flow is not negligible.

Our KLUN sample (6600 spirals) is presently the largest homogeneous catalogue for using the Tully-Fisher (TF) relation as distance indicator, to study both the Hubble constant and peculiar velocities at the scale of the local Universe up to z=0.025.

We calculate B-, R- and I-band internal extinction A(λ)i (absorption + scattering) for spirals consisting of an exponential dust layer, a stellar disk and a bulge. The result is applied to local calibrators and cluster spirals (Virgo and Ursa Major) to examine whether or not the wavelength dependence of the relative zero point difference of Tully-Fisher (TF) relations between for local calibrators and for cluster spirals (Pierce & Tully, 1992) could be accounted for by a variation of A(λ)i on the optical depth of galaxies. The extinction is calculated using Monte-Carlo simulations prescribed by Bianchi et al. (1996). For the extinction curve we adopted the one of Cardelli et al. (1989). It is found that a differential extinction A(R or I)i – A(B)i as a function of the optical depth σ(B) has finite upper limits of ∼ 0.3–0.5 mag, depending on an inclination of the spiral. These limits are generally smaller than the offset of the TF relative zero point difference. This indicates that the offset may be fully due to an intrinsic color difference between local calibrators and cluster galaxies, or else that the current extinction model is yet to realize a practical extinction process or geometrical configuration of spirals.

My goal is to summarize our understanding of the cosmic microwave background radiation (CMBR) at this interesting moment after the detection of fluctuations in the background and before the next generation of satellite experiments. I begin by listing recent reviews and papers on the spectrum of the CMBR. I then sketch the current theoretical description of the power spectrum of fluctuations in the CMBR. Astronomical foregrounds and the nature of secondary fluctuations are treated next. Then I turn to observations, with special emphasis on the final results of the COBE–DMR experiment, on the growing evidence for ΔT/T = 2–3 × 10−5 fluctuations at degree scales, and on what they tell us about cosmological parameters.

After the sensational discovery of Cosmic Microwave Background (CMB) anisotropies by Differential Microwave Radiometer (DMR) boarded on the Cosmic Background Explore (COBE) (Smoot et al. 1992), the number of observational data of temperature fluctuations have been rapidly increasing (see e.g., White, Scott and Silk 1994) together with the understanding of physical processes of evolution of CMB anisotropies. Nowadays, CMB anisotropies are becoming one of the key observational object in the modern cosmology. CMB anisotropies provide us direct information at last scattering surface, i.e., redshift z ≈ 1000. Since the shape of the angular power spectrum of CMB anisotropies is highly sensitive to geometry of the universe, cosmological models and cosmological parameters, i.e., density parameter Ω0, Hubble constant h which is normalized by 100km/s/Mpc, cosmological constant Λ, baryon density ΩB and so on, CMB anisotropies are expected to be a new tool to understand our universe. Moreover, we can obtain information of thermal history of the universe after recombination (through the formation of secondary fluctuations and damping of primary fluctuations), physics of clusters of galaxies (through the Sunyaev-Zeldovich effect) and non-linear structure of the universe (through the gravitational lensing effect) from CMB anisotropies.

The CMB is already one of the pillars of the Big Bang model. However it may also become our most powerful tool to distinguish contending models and to determine their cosmological parameters. To realize this goal, more than 20 observational groups and two new satellites are gearing up to make precise measurements of the CMB at small angular scales. In such a situation it is important to keep track of what the CMB data can already say about cosmological parameters.

Current CMB data can already be used to constrain cosmological parameters. The results are model dependent. We have obtained contraints on Hubble's constant h and the density of the Universe Ωo in the context of open and critical density CDM models with Λ = 0. In critical density models we obtain h = 0.30+0.18−0.07. This low value is inconsistent with direct measurements of h but fully consistent with four other cosmological measurements: Big Bang nucleosynthesis, cluster baryonic fraction, age constraints from globular clusters and limits on the shape parameter Γ of matter power spectra (in Ωo = 1 models). If Ωo is left as a free parameter the constraints on h are less restrictive: h = 0.40+0.57−0.14. This is fully consistent with local h measurements and the four other cosmological measurements mentioned above. The best-fit density is Ωo = 0.85 and we set an upper limit of Ωo > 0.4 at ∼ 95% CL.

At this conference Ostriker has claimed that open-CDM models with Ωo ≈ 0.3 and h ≈ 0.70 are compatible with all current data. However our new CMB data analysis rules this model out at more than ∼ 4σ.