Browsing by Author "Engineer, Sunu"

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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.
Formal analysis of two dimensional gravity
(2015-03-11) 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 finally obtain the necessary fluid equations required to describe structure formation. These equations are solved for the density perturbation in both the linearised form and in the spherical top hat model of nonlinear growth. We find 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 different possible ways of getting around this difficulty so that growing structures can be obtained in two dimensional cosmological gravitational simulations and discuss their implications.
Non-linear density evolution from an improved spherical collapse model
(Wiley-Blackwell, 1999-11-30) Engineer, Sunu; Kanekar, Nissim; Padmanabhan, T.
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, δ. The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of δ. The key new idea is a Taylor series expansion in (1/δ) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two point correlation function. Comment: 11 pages, 6 figures. Final version, contains added discussion and modified figures to match the accepted version.
Nonlinear density evolution from an improved spherical collapse model
(2015-03-14) Engineer, Sunu; Kanekar; Padmanabhan, T.
Nonlinear gravitational clustering: Dreams of a paradigm
(American Astronomical Society, 1997-09-08) Padmanabhan, T.; Engineer, Sunu
We discuss the late-time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) that connect the nonlinear and linear two-point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed toward a universal profle that does not change its shape at late times. We begin by clarifying the relation between the density profles of the individual halos and the slope of the correlation function, and we discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profle that preserves the shape at late times, then the correlation function should grow as a2 (in a )\1 universe), even at nonlinear scales. We prove that such exact solutions do not exist ; however, there exists a class of solutions ("psuedolinear profles") that evolve as a2 to a good approximation. It turns out that pseudolinear profles are the correlation functions that arise if the individual halos are assumed to be isothermal spheres. They are also confgurations of mass in which the nonlinear effects of gravitational clustering are a minimum, and hence they can act as building blocks of the nonlinear universe. We discuss the implications of this result.
Scaling Relations for Gravitational Clustering in two Dimensions
(American Astronomical Society, 1997-10-10) Bagla, J. S.; Engineer, Sunu; Padmanabhan, T.
It is known that radial collapse around density peaks can explain the key features of the evolution of a correlation function in gravitational clustering in three dimensions. The same model also makes spe-ciÐc predictions for two dimensions. In this paper we test these predictions in two dimensions with the help of N-body simulations. We Ðnd that there is no stable clustering in the extremely nonlinear regime, but a nonlinear scaling relation does exist and can be used to relate the linear and the nonlinear corre-lation function. In the intermediate regime, the simulations agree with the model.
Structure formation in the quasi-steady state cosmology : A toy model
(American Astronomical Society, 1999-11-01) Nayeri, Ali; Engineer, Sunu; Narlikar, J. V.
The problem of formation of large-scale structure is discussed within the framework of the quasi-steady state cosmology (QSSC). The primary process of creation of matter and the resulting dynamics of ejection of matter from regions of strong gravitational Ðelds play a key role. To understand their workings, a toy model is used, in which from a set of randomly distributed creation centers a new generation of centers is created as part of an iterative algorithm. It is shown that the system develops clusters and voids along with filamentary structure, within a few iterations. The two-point correlation function and density distribution function for these simulations are shown to reproduce the observed clustering of the large-scale structure in the real universe.
Structure formation in the Quasi-Steady state cosmology: A toy model
(2015-03-01) Nayeri, Ali; Engineer, Sunu; Narlikar, J.V.; Hoyle, F.
The problem of formation of large scale structure is discussed within the framework of the Quasi-Steady State Cosmology (QSSC) . The primary process of creation of matter and the resulting dynamics of ejection of matter from regions of strong gravitational fields plays a key role. To understand its working, a toy model is used, in which from a set of randomly distributed creation centres a new generation of centres is created as part of an iterative algorithm. It is shown that the system develops clusters and voids along with filamentary structure, within a few iterations. The two point correlation function and density distribution function for these simulations are shown to reproduce the observed clustering of the large scale structure in the real universe.