Research Publications
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Item Modelling the nonlinear gravitational clustering in the expanding universe(Wiley-Blackwell, 1995-11-02) 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 Formal Analysis of two Dimensional Gravity(American Astronomical Society, 1998-09-17) Engineer, Sunu; Srinivasan, K.; Padmanabhan, T.Several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. In this paper we address the subtle question of ambiguities in the nature of two-dimensional gravity in an expanding background. We take a detailed and formal approach by deriving the equations describing gravity in (D ] 1) dimensions using the action principle of Einstein. We then consider the Newtonian limit of these equations and Ðnally obtain the necessary Ñuid equations required to describe structure formation. These equations are solved for the density perturbation in both the linearized form and in the spherical top-hat model of nonlinear growth. We Ðnd that, when the special case of D \ 2 is considered, no structures can grow. We therefore conclude that, within the frame work of Einstein's theory of gravity in (2 ] 1) dimensions, formation of structures cannot take place. Finally, we indicate the di erent possible ways of getting around this difficulty, so that growing struc-tures can be obtained in two-dimensional cosmological gravitational simulations, and discuss their implications.