The debate about the possible smoothness of the Universe on large scales as opposed to an unbounded fractal hierarchy has been the subject of increasing interest in recent years. The controversy arises as a consequence of different statistical analyses performed on surveys of galaxy redshifts. I review the observational evidence supporting the idea that a gradual transition occurs in the galaxy distribution: from a fractal regime at small scales to large scale homogeneity.

A summary is given of the calibration of the Cepheid scale required in the derivation of distances from observations at V and I, as in the HST work on extragalactic Cepheids. There is some evidence that a small metallicity correction may be necessary in deriving distances in this way. The evidence for this comes both from observations of Cepheids of different metallicities and from a comparison of the LMC distance modulus derived from Cepheids and that derived by other methods.

As this conference has attested to, cosmology is a rapidly maturing field, currently experiencing a very healthy and vigorous confrontation between theory and experiment. This rapid progress in many different areas of cosmology has not removed the longstanding interest in measuring many of the fundamental cosmological parameters - rather, the increasingly detailed predictions of current theory highlight the critical importance of independently, accurately measuring the cosmological parameters which define the basic model for the dynamical evolution of the Universe. I present here the final results of the Hubble Space Telescope (HST) Key Project to measure the Hubble constant, summarizing our method, the results and the uncertainties. The Key Project results are based on a Cepheid calibration of several secondary distance methods applied over the range of about 60 to 400 Mpc. Based on the Key Project Cepheid calibration and its application to five secondary methods (type Ia supernovae, the Tully-Fisher relation, surface brightness fluctuations, type II supernovae, and the fundamental plane for elliptical galaxies), a combined value of H0 = 72 ± 8 km/sec/Mpc is obtained. Comparing to current estimates of the ages of Galactic globular clusters, an age conflict is avoided for this high a value of H0 if we live in a Λ-dominated (or other form of dark energy) universe.

The methodology involved in deriving the Hubble Constant via the calibration of the corrected peak luminosities of Type Ia supernovae (SNe) is reviewed. We first present a re-analysis of the Calán-Tololo (C-T) and Center for Astrophysics (CfA) Type Ia SN surveys. Bivariate linear least squares and quadratic boot-strapped fits in peak apparent magnitude and light curve shape are employed to correct this heterogeneous sample of peak apparent magnitudes, resulting in an homogeneous (and excellent) secondary distance indicator: the so-called corrected peak luminosity. We next provide an empirical calibration for this corrected luminosity, using Cepheid-based distances for seven nearby spiral galaxies host to Type Ia SNe. Included in this sample is the spectroscopically peculiar SN 1991T (in NGC 4527), whose corrected peak luminosity is shown to be indistinguishable from that of so-called “normal” SNe. A robust value of the Hubble Constant is derived and shown to be H0=73±2(r)±7(s)km s-1 Mpc-1.

The 0th, 1st and 2nd derivatives of a “Fermat potential” give the three D's of gravitational lensing: delay, deflection and distortion. Observations of these delays, deflections and distortions for doubly and quadruply imaged quasars give estimates of Hubble's constant, H0. The single largest contribution to the uncertainty in H0 arises from the difficulty in constraining the degree of central concentration of the lensing potential. Fortunately, astronomers have spent a good deal of effort over the past quarter century addressing just this question. If galaxies at z = 0.5 are like nearby galaxies, the associated systematic uncertainty in H0 is less than 10%. The expected lens-to-lens scatter is 20%. Results from three particularly well constrained systems are reported.

This talk presents a summary of the most recent results from microwave and millimeter-wave surveys of the Sunyaev-Zeldovich Effect (SZE) in massive clusters of galaxies. The SZE is caused by Compton scattering of low-energy CMB photons off high-temperature ionized gas in cluster atmospheres, and is a direct measurement of the baryon content of the intracluster medium. New results from the Chicago-BIMA SZE survey of Carlstrom et al., the Penn-OVRO SZE program of Mason et al., and the Caltech-CBI SZE project of Padin et al. are discussed, along with prospects for future imaging and interferometric studies of clusters to pin down the astrophysical properties of cluster baryons and dark matter as well as possible constraints on cosmological parameters.

We present preliminary results of a follow-up survey which aims to characterise in detail those galaxies which hosted Type Ia supernovae found by the Supernova Cosmology Project. Our survey has two components: Hubble Space Telescope imaging with STIS and Keck spectroscopy with ESI, the goal being to classify each host galaxy into one of three broad morphological/spectral classes and hence to investigate the dependence of supernovae properties on host galaxy type over a large range in redshift. Of particular interest is the supernova Hubble diagram characterised by host galaxy class which suggests that most of the scatter arises from those occurring in late-type irregulars. Supernovae hosted by (presumed dust-free) E/SO galaxies closely follow the adopted SCP cosmological model. Although larger datasets are required, we cannot yet find any significant difference in the light curves of distant supernovae hosted in different galaxy types.

The earliest spectrum available of a well-observed, local type Ia SN, the UV-optical spectrum of SN 1990N obtained 14 days before B maximum, was modelled with a Monte Carlo code in order to determine its epoch and consequently the rise time from explosion to B max, which is important for fitting template light curves. If a standard density distribution and composition for the SN ejecta are used, and the Cepheid distance modulus to the host galaxy, NGC4639 in the Virgo cluster, μ = 32.0, is adopted, the spectrum is best reproduced for an epoch t = 5.5 ± 1 days, implying for the SN a rise time of 19.5 ± 1 days. For a shorter μ, t is smaller, but for a T-F distance μ = 31.4 the solution is not consistent.

I review simultaneous constraints on the cosmological parameters Δ0 and Ω0 from gravitational lensing. The emphasis is on systematic extragalactic surveys for strong gravitational lenses, mainly the largest and best-defined such survey, JVAS/CLASS.

A non-zero cosmological constant is only one of many possible explanations for the observed accelerating expansion of the Universe. Any smoothly distributed, “dark” energy with a significant negative pressure can drive the acceleration. One possible culprit is a dynamical scalar field, but there are many less popular models such as tangled cosmic strings or domain walls. Soon theorists are likely to think up a number of new energies that can accelerate the expansion, meaning that only better observations can solve this question. Dark energy can be parameterized by its equation of state, w = p/ρ, which in the most general form can vary over time. Unlike the CMB, supernova observations cover a range of redshift so they can, in principle, probe the variation in the equation of state of the unknown component. The current SN observations loosely constrain the equation of state to w < −0.6, ruling out non-intercommuting strings and textures (w = −1/3), but consistent with a cosmological constant (w = −1). The constraints achievable from future large SN surveys are limited by our ability to understand systematic effects in SN Ia luminosities. But a large sample of supernovae reaching out to z ˜ 2 should at least discriminate between a cosmological constant and a dynamical scalar field as the source of the observed acceleration.

I describe a new class of quintessence+CDM models in which late time scalar field oscillations can give rise to both quintessence and cold dark matter. Additionally, a versatile ansatz for the luminosity distance is used to reconstruct the quintessence equation of state in a model independent manner from observations of high redshift supernovae.

FRIIb radio galaxies can be used as modified standard yardsticks to determine global cosmological parameters; the method is analogous to the use of supernovae type Ia as modified standard candles. FRIIb radio galaxies are observed to very high-redshift; the sources discussed here are fairly evenly distributed in redshift, with redshifts between zero and two. The sources can be used to determine the coordinate distance to high-redshift sources, and thus can constrain global cosmological parameters (just like the use of supernova type Ia to determine the coordinate distance, or luminosity distance, to high-redshift sources). Current constraints on global cosmological parameters and on quintessence obtained using FRIIb radio galaxies are presented.

The determinations of the mass density parameter Ω0 are examined with a particular emphasis given to the new cosmic microwave background (CMB) experiments. It is shown that the Ω0 and the Hubble constant H0 from CMB are quite consistent with those from other observations with the aid of the hierarchical structure formation models based on cold dark matter dominance with the cosmological constant that makes the universe flat. The concordance value of Ω0 is 0.25-0.45.

There are now 10 independent observational investigations which have detected systematic weak gravitational lensing of background field galaxies by foreground field galaxies. This effect, known as galaxy-galaxy lensing, results in a very slight (of order 1%) distortion to the intrinsic image shapes of the lensed galaxies. Although small, the galaxy-galaxy lensing signal is coherent about the lens centers and is, therefore, detectable in large data sets via an ensemble average over many candidate pairs of lenses and sources. Here I summarize the results of the recent detections of galaxy-galaxy lensing and discuss some applications that are likely to be implemented in the very near future.

The gravitational lensing rate in a well-defined sample of sources can place strong bounds on the cosmological constant, but only if the lensing optical depth is robustly calculated. Significant progress is likely to be achieved by employing more realistic models to describe the population of lens galaxies. Here we investigate the role of elliptical deflectors in lensing statistics, and their effect on cosmological constraints derived from the JVAS survey. We also evaluate the prospects for constraining the cosmological constant using the much larger CLASS data set.

Improved Sunyaev-Zel'dovich effect data from interferometers and single dishes, and new X-ray data from Chandra and XMM, are allowing a more detailed examination of the Sunyaev-Zel'dovich effect/X-ray technique for the measurement of distance, and hence the Hubble constant. This article reviews progress so far and the current results for H0, and discusses the potential of surveys for the Sunyaev-Zel'dovich effect as tests for cosmological parameters and cluster evolution.

As part of a 4-year Cosmology and Particle Astrophysics (CosPA) Research Excellence Initiative in Taiwan, AMiBA - a 19-element dual-channel 85-105 GHz interferometer array is being specifically built to search for high redshift clusters of galaxies via the Sunyaev-Zeldovich Effect (SZE). In addition, AMiBA will have full polarization capabilities, in order to probe the polarization properties of the Cosmic Microwave Background. AMiBA, to be sited on Mauna Kea in Hawaii or in Chile, will reach a sensitivity of ˜ 1 mJy or 7μK in 1 hour. The project involves extensive international scientific and technical collaborations. The construction of AMiBA is scheduled to starting operating in early 2004.

There is increasing evidence that the majority of dark matter is non-baryonic. Principal candidates are weakly interacting massive particles (WIMPS), axions, and neutrinos. There has been increasing effort on sensitive WIMP searches, motivated in particular by supersymmetry theory, which predicts a stable neutral particle in the mass range 10-1000 GeV. Interactions of these with normal matter would produce low energy nuclear recoils which could be observed by underground detectors capable of discriminating these from background. Current experimental progress is summarised, together with plans for more sensitive experiments. These include gaseous detectors with directional sensitivity, offering the prospect of a ‘dark matter telescope’ which would provide information on the dark matter velocity distribution. Axions could be detected by conversion to microwave photons, and experimental sensitivity is approaching the theoretically-required levels. Relic neutrinos could also form a component of the dark matter if any has a cosmologically significant mass, and the latter could be checked with a new detector able to detect the higher neutrino flavours from a Galactic supernova burst. More distant future possibilities are outlined for direct detection of relic neutrinos by coherent scattering.

One of the most fundamental questions in cosmology is: How much matter is there in the Universe and how is it distributed? Here I show that several independent measures-including those utilizing clusters of galaxies-all indicate that the mass-density of the Universe is low-only ˜20% of the critical density. Recent measurements of the mass-to-light function-from galaxies, to groups, clusters, and superclusters-provide a powerful new measure of the universal density. The results reveal a low density of 0.16±0.05 the critical density. The observations suggest that, on average, the mass distribution follows the light distribution on large scales. The results, combined with the recent observations of high redshift supernovae and the spectrum of the CMB anisotropy, suggest a Universe that has low density (Ωm ⋍0.2), is flat, and is dominated by dark energy.

Clusters constitute a very rich source of information for cosmology. Their present day abundance can be used to found the normalization and the shape of the power spectrum. Clusters can also be used to determine the parameter density of the universe Ω − 0. The evolution of their number density is a powerful cosmological global test of the mean density of the Universe. It is fashionable to claim that the abundance of clusters does not change very much with clusters redshift and therefore favor a low density universe. This is an overstatement and analyses based on the most recent data rather favor a high density universe. The baryon fraction in clusters is an alternative method to derive the mean density of the Universe. Here again, taking into account several biases in the baryon fraction is derived from data, the actual baryon fraction seen in clusters can be reconcilied with a high density universe.