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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 A new indicator of nonlinear gravitational clustering(2015-01-25) Bagla, J. S.Alignment of velocity and acceleration before shell crossing, and later misalignment are used to define velocity contrast, an indicator of dynamical state of matter undergoing gravitational collapse. We use this study bias in clustering properties of dynamically nonlinear mass.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 scalesItem Nonlinear evolution of density perturbation(2015-01-17) Bagla, J. S.; Padmanabhan, T.From the epoch of recombination ( Z ≈103 ) till today, the typical density contrasts have grown by a factor of about 106 in Friedmann universe with Ω = 1. However, during the same epoch the typical gravitational potential has grown only by a factor of order unity. We present theoretical arguments explaining the origin of this approximate constancy of gravitational potential. This fact can be exploited to provide a new, powerful, approximation scheme to study the formation of nonlinear structures in the universe. The essential idea of this method is to evolve the initial distribution of particles using a gravitational potential frozen in time. We carry out this scheme for several standard models including the CDM and HDM and show that the results match quite well with those obtained by exact Numerical simulations. We compute different statistical measures of clustering and compare them for the description of nonlinear evolution. This approximation also provides valuable insight into understanding various features of nonlinear evolution; for example, it provides a simple explanation as to why pancakes remain thin during the evolution even in the absence of any artificial, adhesion-like, damping terms. We also compare this approximation with other schemes like Zeldovich approximation and frozen-flow. Our procedure has a far greater range of validity than the Zeldovic h approximation since it can handle motion across (and inside) caustic properly. Unlike in frozen-flow, actual shell-crossing does occur in the frozen-potential approximation; hence it provides a far more accurate description of the velocity field compared to frozen flow approximation.Item Nonlinear evolution of density perturbations using approximate constancy of gravitational potential(2015-01-13) Bagla, J. S.; Padmanabhan, T.Item Cosmology with tachyon field as dark energy(2011-07-06) Bagla, J. S.; Jassal, H. K.; Padmanabhan, T.We present a detailed study of cosmological effects of homogeneous tachyon matter coexisting with non-relativistic matter and radiation, concentrating on the inverse square potential and the expo- nential potential for the tachyonic scalar field. A distinguishing feature of these models (compared to other cosmological models) is that the matter density parameter and the density parameter for tachyons remain comparable even in the matter dominated phase. For the exponential potential, the solutions have an accelerating phase, followed by a phase with a(t) ∝ t 2/3 as t → ∞. This elimi- nates the future event horizon present in ΛCDM models and is an attractive feature from the string theory perspective. A comparison with supernova Ia data shows that for both the potentials there exists a range of models in which the universe undergoes an accelerated expansion at low redshifts and are also consistent with requirements of structure formation. They do require fine tuning of parameters but not any more than in the case of ΛCDM or quintessence models.