IUCAA Preprints
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Item Aspects of gravitational clustering(2015-03-01) Padmanabhan, T.Several issues related to the gravitational clustering of collisionless dark matter in an expanding universe is discussed. The discussion is pedagogical but the emphasis is on semianalytic methods and open questions-rather than on well established results.Item 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 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 Constraints on the shape of the density spectrum from COBE and galaxy surveys(2014-11-23) Padmanabhan, T.; Narasimha, D.Item Zeldovich approximation and the probability distribution for the smoothed density field in the nonlinear regime(2014-11-23) Padmanabhan, T.; Subramanian, KandaswamyThe study of large-scale structure in the Universe is often based on the observed density distribution of matter smoothed by a suitable filter function. The probability distribution for this smoothed density field in the nonlinear regime is studied using the Zeldovich approximation. When the shear term of the velocity field is not too large, one can obtain a reasonably good analytic approximation to this probability distribution. The properties of this distribution are discussed and compared with other attempts along similar lines.