Post recombination density perturbations have been studied in a two-component matter-radiation universe. The study has been carried out for variable matter and radiation densities. The possibility of the existence of different kinds of neutrinos in addition to the electronic, muonic and taonic has been considered and conclusions have been drawn as to the upper limit of the radiation density for different values of Ω_m.

The description of gravitational clustering is essentially statistical but its origin is dynamical. Hence both aspects of clustering: dynamical and statistical, must be understood in order to arrive at a proper appreciation of the subject of gravitational instability and the formation and evolution of the large scale structure of the Universe. Key dynamical aspects of gravitational clustering such as the Zeldovich approximation and its extension — the adhesion model are reviewed. Statistical indicators of clustering such as the correlation function and percolation theory, as applied to the large scale structure of the Universe have also been focussed on.

The inflationary Universe resolves some of the most outstanding issues of standard cosmology including the horizon and flatness problems and the origin of density fluctuations in the Universe. Inflationary models also predict the existence of a relic gravity wave background. Both gravity waves and density fluctuations induce fluctuations in the cosmic microwave background (CMB), the discovery of large angle anisotropies in the CMB having the scale invariant spectrum predicted by inflationary models has fuelled the hope that the inflationary scenario may indeed provide the correct description of the very early Universe. Upcoming large scale galaxy surveys (SDSS & 2dF) and CMB missions (MAP, Planck Surveyor) will further probe the inflationary scenario by throwing light on the origin and evolution of large scale structure in the Universe.

The astroparticle physics working group witnessed intense discussion and activity covering a broad range of topics ranging from supergravity and baryogenesis to compact stars and the large scale structure of the Universe. A summary of some of the subject areas in which collaborations were initiated during WHEPP-5 is presented below.

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.

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.

I present a short overview of current observational results and theoretical models for a cosmological constant. The main motivation for invoking a small cosmological constant (or A-term) at the present epoch has to do with observations of high redshift Type Ia supernovae which suggest an accelerating universe. A flat accelerating universe is strongly favoured by combining supernovae observations with observations of CMB anisotropies on degree scales which give the ‘best-fit’ values Θ_A ⋍ 0.7 and Θ_m ⋍ 0.3. A time dependent cosmological A-term can be generated by scalar field models with exponential and power law potentials. Some of these models can alleviate the ‘fine tuning’ problem which faces the cosmological constant.

This talk presents a brief overview of recent results pertaining to the cosmological constant ‘A’. I summarize the observational situation focussing on observations of high redshift Type Ia supernovae which suggest A > 0. Observations of small angular anisotropies in the cosmic microwave background complement Type Ia supernovae observations and both CMB and Sn can be combined to place strong constraints on the value of A. The presence of a small A-term increases the age of the universe and slows down the formation of large scale structure. I also review recent theoretical attempts to generate a small A-term at the current epoch and a model independent approach for determining the cosmic equation of state.