1995 (IPP)
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Item Crisis in cosmology : observational constraints on Ω and H0(2015-02-07) Bagla, J. S.; Padmanabhan, T.; Naralikar, J.V.Two decades ago, in an article in Nature, Gunn and Tinsley1 had reviewed the then available data in cosmology to conclude: " New Data on the Hubble diagram, combined with constraints on the density of the universe and the ages of galaxies, suggest that the most plausible cosmological models have a positive cosmological constant, are closed, too dense to make deuterium in the big bang, and will expand for ever ... ". Thanks to new technology of observations and fresh inputs from particle physics, cosmology has since advanced on both observational and theoretical fronts. The standard hot big bang model has, if at all, become more deeply rooted in cosmology today than in 1975. It is therefore opportune that we take fresh stock of the cosmological situation today and examine the observational and theoretical constraints as they are now. Not surprisingly, some of the issues discussed by Gunn and Tinsley [ op. cit.] continue to be relevant today whereas fresh ones have replaced the rest. The purpose of this article is to carry out a similar exercise in the modern cosmological framework. The bottom line in this review is that despite the availability of the cosmological constant as an extra parameter for flat Friedmann models, the allowed parameter space for such models has shrunk drastically. The observations that we will consider here include the ages of globular clusters, measurement of Hubble's constant, abundance of rich clusters of galaxies, fraction of mass contributed by baryons in rich clusters and abundance of high red shift objects. We begin with a brief description of the theoretical models in standard cosmology. For the notation the reader may refer to standard textbooks2 •Item String-dust perfect fluid in singularity-free models(2015-01-27) Padmanabhan, T.We have attempted to incorporate string-dust in perfect fluid singularity free inhomogeneous models. It turns out the stiff fluid can only sustain inclusion of string-dustItem Gravitational dynamics in an expanding universe(2015-01-27) Padmanabhan, T.The dynamical evolution of collisionless particles in an expanding background is described. After discussing qualitatively the key features, the gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in hierarchical models. This analysis leads to results which are in good agreement with numerical simulations thereby providing an explanation for numerical results. The ideas presented here will also serve as a powerful analytical tool to investigate nonlinear clustering in different models. Several implications of the result are discussedItem Modelling the nonlinear gravitational clustering in the expanding universe(2015-01-25) Padmanabhan, T.The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in heirarchical models. This analysis leads to results which are in good agreement with numerical simulations thereby providing an explanation for numerical results. The ideas presented here will also serve as a powerful anlytical tool to investigate nonlinear clustering in different models. Several implications of the result are discussed.Item A new statistical indicator to study nonlinear gravitational clustering and structure formation(2015-01-25) Bagla, J. S.; Padmanabhan, T.In an Ω = 1 universe dominated by nonrelativistic matter, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality is unity and velocity and force field are equal. The Zeldovich approximation extends this feature beyond the linear regime, until formation of pancakes. Nonlinear clustering which takes place after the breakdown of Zeldovich approximation, breaks this relation and the mismatch between these two vectors increases as the evolution proceeds. We suggest that the difference of these two vectors could form the basis for a powerful, new, statistical indicator of nonlinear clustering. We define an indicator called velocity contrast, study its behaviour using N-Body simulations and show that it can be used effectively to delineate the regions where nonlinear clustering has taken place. We discuss several features of this statistical indicator and provide simple analytic models to understand its behaviour. Particles with velocity contrast higher than a threshold have a correlation function which is biased with respect to the original sample. This bias factor is scale dependent and tends to unity at large scales