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Varun Sahni

Publications and source records attributed to Varun Sahni.

99 records · Page 6Linked to original sources
arXiv1996

Probing Large Scale Structure using Percolation and Genus Curves

We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the density field shows an increasingly pronounced departure from Gaussianity reflected in the changing shape of the percolation curve and the changing amplitude and shape of the genus curve. Both genus and percolation curves differentiate between the connectedness of overdense and underdense regions if plotted against the density. When plotted against the filling factor the percolation curve alone retains this property. The genus curve shows a pronounced decrease in amplitude caused by phase correlations in the non-linear regime. Both genus and percolation curves provide complementary probes of large scale structure topology and can be used to discriminate between models of structure formation and the analysis of observational data such as galaxy catalogs and MBR maps.

astro-ph↗
arXiv1995

Approximation Methods for Non-linear Gravitational Clustering

We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. These methods can be classified into five types: (i) simple extrapolations from linear theory, such as the high--peak model and the lognormal model; (ii) {\em dynamical} approximations, including the Zel'dovich approximation and its extensions; (iii) non--linear models based on purely geometric considerations, of which the main example is the Voronoi model; (iv) statistical solutions involving scaling arguments, such as the hierarchical closure {\em ansatz} for BBGKY, fractal models and the thermodynamic model of Saslaw; (v) numerical techniques based on particles and/or hydrodynamics. We compare the results of full dynamical evolution using particle codes and the various other approximation schemes. To put the models we discuss into perspective, we give a brief review of the observed properties of galaxy clustering and the statistical methods used to quantify it, such as correlation functions, power spectra, topology and spanning trees.

astro-ph↗
arXiv1995

EVOLUTION OF THE POTENTIAL IN COSMOLOGICAL GRAVITATIONAL CLUSTERING

The potential is a constant to linear order in cosmological gravitational clustering. In this Letter we present results of testing the conjecture, proposed by Pauls and Melott (1995), that the effect of nonlinear evolution on the potential can be better described by smoothing it on the scale of nonlinearity. We show two-dimensional simulations consisting of an N-body code in which particles are accelerated not by their mutual attraction, but by the gradient of the initial potential smoothed on the current scale of nonlinearity. This approximation produces results considerably improved over using a constant potential to move particles, and it is generally better than any approximation we have tested, lending further support to the smoothing description of the evolved potential.

astro-ph↗
arXiv1994

The Evolution of Voids in the Adhesion Approximation

We apply the adhesion approximation to study the formation and evolution of voids in the Universe. Our simulations -- carried out using 128$^3$ particles in a cubical box with side 128 Mpc -- indicate that the void spectrum evolves with time and that the mean void size in the standard COBE-normalised Cold Dark Matter (hereafter CDM) model with $h_{50} = 1,$ scales approximately as $\bar D(z) = {\bar D_0\over \sqrt {1+z}},$ where $\bar D_0 \simeq 10.5$ Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way towards reconstructing the form of the primordial potential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in $k$-space cutoff we find that, the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments merge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitational potential. A central result of this paper is that

astro-ph↗
arXiv1994

Non-Linear Approximations to Gravitational Instability: A Comparison in the Quasi-Linear Regime

We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of non-Gaussianity which can be characterised by a set of numbers $S_p$ describing connected moments of the density field at the lowest order in $<δ^2>$: $<δ^n>_c \simeq S_n<δ^2>^{n-1}$. Generalizing earlier work by Bernardeau (1992) we develop an ansatz to evaluate all $S_p$ in a given approximation by means of a generating function which can be shown to satisfy the equations of motion of a homogeneous spherical density enhancement in that approximation. On the basis of the values of we show that approximations formulated in Lagrangian space (such as the Zeldovich approximation and its extensions) are considerably more accurate than those formulated in Eulerian space such as the Frozen Flow and Linear Potential approximations. In particular we find that the $n$th order Lagrangian perturbation approximation correctly reproduces the first $n+1$ parameters $S_n$. We also evaluate the density probability distribution function for the different approximations in the quasi-linear regime and compare our results with an exact analytic treatment in the case of the Zeldovich approximation.

astro-ph↗
arXiv1993

Post-COBE predictions for Inflationary Gravity Wave and Density Perturbation spectra

We assess the relative contribution to the COBE - measured microwave anisotropy arising both from relic gravity waves as well as primordial density perturbations originating during inflation. We show that the gravity wave contribution to the CMBR anisotropy depends sensitively upon $n$ -- the primordial spectral index ($\dk^2 \propto k^n$), increasing as $n$ deviates from a Harrison - Zeldovich spectrum (n = 1). As a result, for $n < 0.84$ the contribution from gravity waves towards $δT/ T $ is greater than the corresponding contribution from density perturbations, whereas for $n > 0.84$ the reverse is true. ($ n = 0.84$ corresponds to an expansion index $p = 13.5$ in models with power-law inflation $a \propto t^p$. ) Our results show that for a scale-invariant Harrison-Zeldovich spectrum generated by chaotic inflation, gravity waves contribute approximately $24\%$ to the CMBR anisotropy measured by COBE. Applying our results to the cold dark matter scenario for galaxy formation, we find that in general CDM models with tilted power spectra ($n < 1$), require the biasing parameter to be greater than unity, on scales of $16h_{50}^{-1} Mpc$. We also obtain an expression for the COBE - normalised amplitude and spectrum of the stochastic gravity wave background and compare it with the sensitivity of planned laser-interferometer gravity wave detectors.

hep-ph↗
arXiv1992

Quantum effects near a point mass in 2+1 dimensional gravity

We investigate the behaviour of classical and quantum fields in the conical space-time associated with a point mass in 2+1 dimensions. We show that the presence of conical boundary conditions alters the electrostatic field of a point charge leading to the presence of a finite self-force on the charge from the direction of the point mass exactly as if the point mass itself were charged. The conical space-time geometry also affects the zero point fluctuations of a quantum scalar field leading to the existence of a vacuum polarisation --- $\langle T_\mn \rangle$, in the 2+1 dimensional analog of the Schwarzschild metric. The resulting linearised semi-classical Einstein equations --- $G_\mn = 8 πG \langle T_\mn \rangle$, possess a well defined Newtonian limit, in marked contrast to the classical case for which no Newtonian limit is known to exist. An elegant reformulation of our results in terms of the method of images is also presented. Our analysis also covers the non-static de Sitter--Schwarzschild metric in 2+1 dimensions, in which in addition to the vacuum polarisation, a non-zero vacuum flux ofenergy -- $\langle T_{rt} \rangle $ is also found to exist.As part of this analysis, we evaluate the scalar field propagator in an $n$-dimensional de Sitter space,

hep-ph↗
arXiv1992

Density Perturbations,Gravity Waves and the Cosmic Microwave Background

We asses the contribution to the observed large scale anisotropy of the cosmic microwave background radiation, arising from both gravity waves as well as adiabatic density perturbations, generated by a common inflationary mechanism in the early Universe. We find that for inflationary models predicting power law primordial spectra %$a(t) \propto t^p, p > 1$, $\dk^2 \propto k^n$, the relative contribution to the quadrupole anisotropy from gravity waves and scalar density perturbations, depends crucially upon $n$. For $n < 0.87$, gravity waves perturb the CMBR by a larger amount than density perturbations, whereas for $n > 0.87$ the reverse is true. %For nearly exponential inflation, on the other hand, the contribution to the %microwave anisotropy from scalar density perturbations always exceeds %that due to gravity waves. Normalising the amplitude of the density perturbation spectrum at large scales, using the observed value of the COBE quadrupole, we determine $(δM /M)_{16}$ -- the rms density contrast on scales $\sim 16 h_{50}^{-1}$ Mpc, for cosmological models with cold dark matter. We find that for $n < 0.75$, a large amount of biasing is required in order to reconcile theory with observations.

hep-ph↗