Research Papers (TP)
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Item Crisis in cosmology: Observational constraints on Omega and H(Overseas Publishers Association, 1996-03-18) Bagla, J. S.; Padmanabhan, T.; Narlikar, J. V.This review of recent observations of cosmological interest seeks to take stock of how they constrain the standard hot big bang models with or without inflation. We look at two specific series indicative of this class of models. In one series the flatness condition of inflation requires that the density parameter shall be unity. Of late this statement has been relaxed somewhat to include the cosmological constant also as a contributor to the density parameter. Hence we ha»e used this "generalised" flatness condition. The other series of models does not need (be cosmological constant but assumes that the curvature parameter k = -1. Both these models are currently being pushed as "the" models of the universe. The observational constraints used by us are the measurements of the Hubble constant and the deceleration parameter, the ages of globular clusters, the abundance of primordial deuterium, the abundance of rich clusters, the baryon content of galaxy clusters and the abundance of high rsdshift objects. These constraints essentially limit the allowed values of the cosmological parameters. Our findings are that with measurements within their quoted error bars, the available parameter space has shrunk to negligible proportions. For survival of the standard models, therefore, one needs to take recourse to two normally unpalatable steps: (i) to doubt the existing error bars and hope to expand them and (ii) to fine-tone the theoretical parameters so that they fall within the available space. This is the essence of our perception of the crisis in cosmology.Item Cosmology Today: Models and constraints(Indian Academy of Sciences, 1995-03-12) Padmanabhan, T.Cosmological models for structure formation are severely constrained by several of the recent observational results. we now have observations which probe the power spectrum of fluctuations from about 0.5h-1 Mpc. these probes and the constraints they imply on models for structure formation are reviewed.Item Cosmological N-Body Simulations(Indian Academy of Sciences, 1997-08-12) Bagla, J. S.; Padmanabhan, T.In this review we discuss Cosmological N-Body codes with a special emphasis on Particle Mesh codes. We present the mathematical model for each component of N-Body codes. We compare alternative methods for computing each quantity by calculating errors for each of the components. We suggest an optimum set of components that can be combined reduce overall errors in N-Body codes.Item Constraints on the shape of the density spectrum from COBE and galaxy surveys(Wiley-Blackwell, 1992-10-28) Padmanabhan, T.; Narasimha, D.Item Inverse Compton Scattering – Revisited(Indian Academy of Sciences, 1996-11-30) Padmanabhan, T.The inverse Compton scattering of high energy electrons by photons is discussed and a simple derivation of the total power radiated is presented. The derivation is completely classical and exhibits clearly why similar formulas are applicable in the case of inverse compton scattering and synchroton radiation.Item Inflation for astronomers(Annual Reviews Inc., 1991-03-12) Narlikar, J. V.; Padmanabhan, T.Item Hypothesis of path integral duality. I. Quantum gravitational corrections to the propagator(American Physical Society, 1998-05-15) Padmanabhan, T.The action for a relativistic free particle of mass m receives a contribution -mR(x,y) from a path of length R(x,y) connecting the events xi and yi. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass m in any background spacetime. If one of the effects of quantizing gravity is to introduce a minimum length scale LP in the spacetime, then one would expect the segments of paths with lengths less than LP to be suppressed in the path integral. Assuming that the path integral amplitude is invariant under the “duality” transformation R→LP2/R, one can calculate the modified Feynman propagator in an arbitrary background spacetime. It turns out that the key feature of this modification is the following: The proper distance (Δx)2 between two events, which are infinitesimally separated, is replaced by Δx2+LP2; that is, the spacetime behaves as though it has a “zero-point length” of LP. This equivalence suggests a deep relationship between introducing a “zero-point length” to the spacetime and postulating invariance of path integral amplitudes under duality transformations. In Schwinger’s proper time description of the propagator, the weightage for a path with proper time s becomes m(s+LP2/s) rather than as ms. As to be expected, the ultraviolet behavior of the theory is improved significantly and divergences will disappear if this modification is taken into account. Implications of this result are discussed.Item Hypothesis of path integral duality. II. Corrections to quantum field theoretic results(American Physical Society, 1998-07-13) Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.In the path integral expression for a Feynman propagator of a spinless particle of mass m, the path integral amplitude for a path of proper length R(x,x'\|gμν) connecting events x and x' in a spacetime described by the metric tensor gμν is exp \{-[m R(x,x'\|gμν)]\}. In a recent paper, assuming the path integral amplitude to be invariant under the duality transformation R-->(L2P/R), Padmanabhan has evaluated the modified Feynman propagator in an arbitrary curved spacetime. He finds that the essential feature of this ``principle of path integral duality'' is that the Euclidean proper distance (Δx)2 between two infinitesimally separated spacetime events is replaced by [(Δx)2+4L2P]. In other words, under the duality principle the spacetime behaves as though it has a ``zero-point length'' LP, a feature that is expected to arise in a quantum theory of gravity. In Schwinger's proper time description of the Feynman propagator, the weightage factor for a path with a proper time s is exp [-(m2s)]. Invoking Padmanabhan's ``principle of path integral duality'' corresponds to modifying the weightage factor exp [-(m2s)] to exp \{-[m2s+(L2P/s)]\}. In this paper, we use this modified weightage factor in Schwinger's proper time formalism to evaluate the quantum gravitational corrections to some of the standard quantum field theoretic results in flat and curved spacetimes. In flat spacetime, we evaluate the corrections to (1) the Casimir effect, (2) the effective potential for a self-interacting scalar field theory, (3) the effective Lagrangian for a constant electromagnetic background and (4) the thermal effects in Rindler coordinates. In arbitrary curved spacetime, we evaluate the corrections to (1) the effective Lagrangian for the gravitational field and (2) the trace anomaly. In all these cases, we first briefly present the conventional result and then go on to evaluate the corrections with the modified weightage factor. We find that the extra factor exp [-(L2P/s)] acts as a regulator at the Planck scale thereby ``removing'' the divergences that otherwise appear in the theory. Finally, we discuss the wider implications of our analysis.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 Modelling the evolution of correlation functions in gravitational clustering(Wiley-Blackwell, 1997-05-13) Munshi, Dipak; Padmanabhan, T.Padmanabhan has suggested a model to relate the nonlinear two - point correlation function to the linear two - point correlation function. In this paper, we extend this model in two directions: (1) By averaging over the initial Gaussian distribution of density contrasts, we estimate the spectral dependence of the scaling between nonlinear and linear correlation functions. (2) By using a physically motivated ansatz, we generalise the model to N-point correlation functions and relate the nonlinear, volume averaged, N-point correlation function ξN(x,a) with linearly extrapolated volume averaged 2-point correlation function ξ2(l,a) evaluated at a different scale. We compare the point of transition between different regimes obtained from our model with numerical simulations and show that the spectral dependence of the scaling relations seen in the simulations can be easily understood. Comparison of the calculated form of ξN with the simulations show reasonable agreement. We discuss several implications of the results.