There is some consensus emerging on the values of the basic parameters of classical cosmology. The baryon number density estimated from the light element abundance or X-ray gas in galaxy clusters tends towards 5% of closure density; the dark matter content based on a number of independent methods appears to be somewhat less than half the closure density; Hubble constant obtained from local measurements, gravitational lens or Sunyaev Zeldovich method are all probably centred around 60 km/sec/Mpc and the age of the Universe is generally agree to be around 14 Gyr — all specified with bearable error bars. The supernova projects and CMBR anisotropy together favour a finite cosmological constant, and gravitational lens statistics support the same conclusion.

HST data on Cepheid variables in one Virgo Cluster spiral galaxy is re-analyzed, taking into account flux-limited incompleteness in the sample and calibration of the period-luminosity relation in the relevant period range. Distance to the Virgo Cluster is estimated to be 19.6 ± 1.7 (random) ± 2.6 (systematic) Mpc.

I briefly review the observational evidence for a small cosmological constant at the present epoch. This evidence mainly comes from high redshift observations of Type 1a supernovae, which, when combined with CMB observations strongly support a flat Universe with Ω_m + Ω_A ⋍ 1. Theoretically a cosmological constant can arise from zero point vacuum fluctuations. In addition ultra-light scalar fields could also give rise to a Universe which is accelerating driven by a time dependent Λ-term induced by the scalar field potential. Finally a Λ dominated Universe also finds support from observations of galaxy clustering and the age of the Universe.

Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lemaître (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (‘open’) FL universe is not necessarily infinite in volume.

Multiply connected flat and hyperbolic models are, in general, as consistent with present observations on scales of 1–20 h⁻¹ Gpc as are the corresponding simply connected flat and hyperbolic models. The methods of detecting multiply connected models (MCM’s) are presently in their pioneering phase of development and the optimal observationally realistic strategy is probably yet to be calculated. Constraints against MCM’s on ∼1–4 h⁻¹ Gpc scales have been claimed, but relate more to inconsistent assumptions on perturbation statistics rather than just to topology. Candidate 3-manifolds based on hypothesised multiply imaged objects are being offered for observational refutation.

The theoretical and observational sides of this rapidly developing subject have yet to make any serious contact, but the prospects of a significant detection in the coming decade may well propel the two together.

The theory of generation of CMBR temperature and polarization fluctuations is briefly reviewed. Also discussed is the present status of observations and the nature of future surveys.

In re-ionized models, the measurement of polarization of CMBR can be a good criterion to narrow down the parameter space for cosmological models. A Vishniac-type effect in second order polarization over arc minute scales has been calculated. It has been shown that while the effect is very small (∼10⁻²µK) for CDM models, it can be significant (∼0.3µK) for some isocurvature models.

For cold dark matter models, images of temperature fluctuations in the cosmic microwave background (CMB), due to Sunyaev Zel’dovich (SZ) effect have been been simulated taking a cosmolgical distribution of clusters into account. All the models are normalised to the 4-year COBE data. The image statistics are compared with the ATCA limits on arcmin scale anisotropy. The comparison appears to favour low-Ω₀ open universe models.

We briefly discuss some aspects of the problem of forming large scale structures in the Universe. The basic picture that initially small perturbations generated by inflation grow by the process of gravitational instability to give the observed structures is largely consistent with the observations. The growth of the perturbations depends crucially on the contents of the Universe, and we discuss a few variants of the cold dark matter model. Many of these models are consistent with present observations. Future observations hold the possibility of deciding amongst these models.

We have carried out a multi-fractal analysis of the distribution of galaxies in the three Northern slices of the Las Campanas redshift survey. In this analysis we have studied the scaling properties of the distribution of galaxies on length scales from 20 h⁻¹ Mpc to 200 h⁻¹ Mpc. Our main results are: (1) The distribution of galaxies exhibits a multi-fractal scaling behaviour over the scales 20 h⁻¹ Mpc to 80 h⁻¹ Mpc, and, (2) the distribution is consistent with homogeneity on the scales 80 h⁻¹ Mpc to 200 h⁻¹ Mpc. We conclude that our results are consistent with the Universe being homogeneous at large scales and the transition to homogeneity occurs somewhere in the range 80 h⁻¹ Mpc to 100 h⁻¹ Mpc.

We consider the geometrical properties of a distribution of matter evolving under gravitational clustering. Such a distribution can be studied using standard statistical indicators such as the correlation function as well as geometrical descriptors sensitive to ‘connectedness’ such as percolation analysis and Minkowski functionals. Applying these methods to N-body simulations and galaxy catalogues we find that the filling factor at the percolation threshold is usually very small reflecting the fact that the Universe consists of a network of filaments and pancakes, the latter being statistically more prominent.

In hierarchical clustering theories, smaller masses generally collapse earlier than larger masses and so are denser on the average. The core of a small mass halo could be dense enough to resist disruption and survive undigested, when it gets incorporated into a bigger object, and determine the halo structure in the inner regions. We examine in this talk the possible consequences of this idea in determining the structure of dark halo cores, by considering, both simple scaling arguments, and a novel fluid approach to self-similar collapse solutions for the dark matter phase space density.

Damped Ly-α systems are the major repository of the observed neutral HI at high redshift. These systems are most efficiently detected via absorption spectra taken against distant QSOs. In this paper, we review some of the observational constraints on the nature of these objects, and also discuss the implications of recent observations of two low redshift damped absorbers, made with the Giant Metrewave Radio Telescope. We find that, for the lowest redshift (z = 0.0912) damped Ly-α system, if the system is a rotating gas disk, then the total associated HI mass has to be less than 2 × 10⁹ M⊙, if the disk is at low inclination angles, and less than 10¹⁰ M⊙ if the system is edge on. All limits are 3σ.

We discuss a few new results which points out the importance of the intergalactic medium as a diagnostic for the formation and evolution of galaxies in the Universe. We discuss the recent studies to determine the power spectrum of fluctuation from QSO-absorption line studies, and then some feedback processes from early galaxies which influence the intergalactic medium.

We have tried to understand the recent observations related to metallicity in Ly-α forest clouds in the framework of the two component model. The model consists of mini-halos having circular velocities smaller than ∼ 55 km s⁻¹, with no star formation and galactic halos with higher circular velocities ≤ 250 km s⁻¹, having clouds, star formation and consequent metal enrichment. We find that even if the mini-halos were chemically enriched by an earlier generation of stars, to have [C/H] ≃ −2.5, the number of C IV lines with column density >10¹² cm⁻², contributed by the mini-halos, at the redshift of 3, would be only about 10% of the total number of lines, for a chemical enrichment rate of (1 + z)⁻³ in the galaxies. Recently reported absence of heavy element lines associated with most of the Ly-α lines with HI column density between 10^13.5 cm⁻² and 10¹⁴ cm⁻² by Lu et al [13], if correct, gives an upper limit on [C/H]= −3.7, not only in the mini-halos, but also in the outer parts of galactic halos. However, the mean value of 7×10⁻³ for the column density ratio of C IV and HI, determined by Cowie and Songaila (1998) for low Ly-α optical depths, implies an abundance of [C/H]= −2.5 in mini-halos as well as most of the region in galactic halos. The redshift and column density distribution of C IV has been shown to be in reasonable agreement with the observations.

Spiral galaxies at moderate redshifts and oriented optimally could form characteristic multiple images of extended background sources from which the mass distribution in the galaxy can be estimated. The absorption profile due to the galaxy provides a reliable tool for the chemical and thermal diagnostic of the lens.

Clusters of galaxies are excellent probes of cosmic structure and evolution. X-ray studies of clusters provide some of their key parameters, viz., temperature of the hot intra-cluster gas, its metallicity, X-ray luminosity and surface brightness giving mass distribution and mass-flow rate in the case of cooling flows. X-ray measurements for a large sample of clusters have lead to estimates of the total gravitating mass in them, which can be compared to the virial masses derived from dynamical considerations and gravitational lensing in some of them. X-ray derived total masses are consistent with masses obtained from the other methods after the effects due to the presence of cooling flows are taken into account in the analyses. Estimated virial masses, lack of evolution in X-ray properties, and detection of several very hot clusters at high redshifts indicate a Universe with a low value (≤ 0.3) for the Ω parameter.

I discuss some compelling suggestions about particles which could be the dark matter in the Universe, with special attention to experimental searches for them.

We review various attempts to create the observed baryon asymmetry of the Universe. In particular, we consider models of GUT baryogenesis, baryogenesis via leptogenesis, the Affleck-Dine mechanism, electroweak baryogenesis and baryogenesis via topological defects and primordial black holes.

Present status of theories of topological defects in particle theory models of the early Universe is discussed. Various consequences of topological defects in cosmology, such as constraints on particle theory models, structure formation etc. are discussed.

It is shown that the minimal left-right symmetric model admits cosmic string and domain wall solutions.

In this talk we discuss a new mechanism of formation of topological defects due to enhanced magnitude oscillations of a complex scalar order-parameter (OP) field during bubble collisions in a first order phase transition.

In this talk we present observation of correlated production of strength one defects and anti-defects formed in isotropic-nematic phase transition in NLC. We find the width σ of the distribution of net winding number, to be in good agreement with the value predicted by the Kibble mechanism for defect production.

This is a review of an alternative cosmology, recently proposed by Fred Hoyle, Geoffrey Burbidge and this author. It begins with a brief discussion of why one needs an alternative cosmology, when the standard hot big bang cosmology is claimed to be doing well. It is argued that the observational and theoretical constraints on the standard big bang cosmology, from various directions, leave a very narrow window, if any, in the parameter space of plausible models. There is thus a strong case for alternative cosmologies. The rest of the review concentrates on one alternative, the quasi steady state cosmology (QSSC) and summarises the recent work on this model. This includes, the theoretical formulation and simple exact solutions of the basic equations, their relationship to various observations, the stability of solutions and the toy model for understanding the growth of structures in the Universe.

In this review, we discuss various cosmological issues related to our Universe from a string theoretic perspective. We analyse the pre-big bang cosmological scenario which appears naturally in this context due to the existence of scale factor duality symmetry in string theory. We then discuss some of the attractive and problematic features of this scenario. Finally, we introduce a method which is powerful enough to search for cosmological solutions in various low energy limits of string theories.

In a space-time with torsion, the action for the gravitational field can be extended with a parity-violating piece. We show how to obtain such a piece from geometry itself, by suitably modifying the affine connection so as to include a pseudo-tensorial part. A consistent method is thus suggested for incorporating parity-violation in the Lagrangians of all matter fields with spin in a space-time background with torsion.

The dynamics of a string near a Kaluza-Klein black hole are studied. Solutions to the geodesic equations are obtained using the world sheet velocity of light as an expansion parameter. For a string falling into a magnetically charged black hole, it is shown that the compact dimension decreases with the world-sheet coordinate τ.

We formulate the data analysis problem for the detection of the Newtonian coalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the same site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is just the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individual detectors. This statistic, therefore, can be interpreted as the signal-to-noise ratio of the network. The overall sensitivity of the network is shown to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the restricted post-Newtonian filters. Finally, our formalism is general enough to be extended, in a straightforward way, to address the problem of detection of such waves from other sources by some other types of detectors, eg., bars or spheres, or even by networks of spatially well-separated detectors.