Research Papers (TP)

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Solutions of scalar and electromagnetic wave equations in the metric of gravitational and electromagnetic waves
(Indian Academy of Sciences, 1977-05-23) Padmanabhan, T.
The wave equation of a scalar field Q and vector potential A' are solved in the background metric of a gravitational wave. The corresponding solutions when the metric is generated by a plane electromagnetic wave is obtained from these solutions. The solution for the scalar wave is discussed in detail. It is found that because of the interaction, two new waves are generated in the lower order approximations. One of them has the same phase dependence as the original wave while the order shows a transient character. There is no interaction when the waves are along the same direction.
Quantum fluctuations and the non-avoidance of singularities in bianchi type I cosmologies
(Springer, 1980-04-28) Padmanabhan, T.
An effective metric is defined and used for analyzing the quantum fluctuations in a classical geometry. Early work showing that quantum conformal fluctuations avoid the classical singularity in the case of spherically symmetric collapse is briefly reviewed it is shown that this result does not extend to anisotropic Bianchi type I cosmology. Here the dispersion in the fluctuations increase to slowly to quench the classical singularity. The singularity persists in the space-time describe by the effective metric.
Quantum fluctuations in conformally flat and Schwarschild spacetimes
(Springer, 1980-12-12) Padmanabhan, T.; Narlikar, J. V.
A general technique is described for dealing with the quantum fluctuations between conformally flat space-times. The second part of the paper deals with the Schwarschild space-time. It is shown there that this space-time is stable against fluctuations of mass, but transitions between two space-times of different masses can be obtained via conformal fluctuations. Purely conformal fluctuations of the Schwarschild metric are, however, damped at the event horizon. Similar conclusions are drawn about the Reissner-Nordstrom space-time.
Stationary states in a quantum gravity model
(Elsevier Science Publishers, 1981-08-17) Padmanabhan, T.; Narlikar, J. V.
A model theory for quantized gravity is discussed where only selected degrees of freedom are quantized. The concept of stationary states is introduced. It is shown that the Planck length arises as a lower bound to the space—time length scale in a natural way.
Quantum Stationary states in Bianchi Universe
(Springer, 1981-10-20) Padmanabhan, T.
A path integral formulation is used in the super space of geometries leading to a model of quantum gravity. It is shown that this method agrees with the standard path integral technique in the special case of Friedman universe. A Shrodinger-like equation is set up, leading to the stationary states. Some solutions to these equations are presented.
Friedmann Universe in a Quantum Gravity model
(Elsevier Science Publishers, 1982-01-11) Padmanabhan, T.
It is shown that, in a model theory of gravity, which quantises only the conformal part, the Robertson-Walker universe has a nonsingular evolution. The method also shows that there arises a lower bound to the physical length scale in any static metric with positive curvature
Symmetry breaking in the early universe and accelerated frames
(IOP Publication, 1982-01-21) Padmanabhan, T.
The formulation of symmetry breaking in a manifold with non-trivial metric is discussed. It is shown that a conformally coupled self-interacting scalar field exhibits spontaneous symmetry breaking in a RW universe. The non-trivial implication of this result to cosmology is discussed. The effective potential in the static space-time is computed to see the effect of one-loop connections. A self-consistent solution is given. In the later part of the paper it is suggested that accelerated frames also have similar effects on the symmetry breaking scheme. Its implications are discussed.
Quantum conformal fluctuations in a singular space-time
(Nature Publishing Group, 1982-02-25) Padmanabhan, T.; Narlikar, J. V.
The cosmological solutions of Einstein's general relativistic equations lead inevitably to space–time singularities1. However, general relativity is only an approximation to a fully quantized theory of gravity and we need to consider whether singularity persists in the quantum domain. Although a full quantum theory of gravity has not yet been developed, we show here that the above question can be tackled in a simplified model where only the conformal degree of freedom is quantized. Previous applications of this technique had shown that in specific cases the quantum conformai fluctuations (QCF) from the classical solutions diverge at the classical singularity, thus rendering the classical solution physically meaningless²,³. Recently one of us (J.V.N. ref. 4) has generalized this result to cover all dust cosmologies. Here we show that this conclusion is applicable to even more general types of cosmological singularities.
On the validity of the geodesic motion near a black hole: A clarification
(Springer, 1982-03-13) Dadhich, Naresh; Padmanabhan, T.
Ot has recently been claimed by Tangherlini that the concept of a test particle following a geodesic breaks down near the Schwarzschild event horizon. We argue that this claim is not valid.
Quantum Conformal Fluctuations and Stationary States
(Plenum Publishing Corporation, 1982-04-07) Padmanabhan, T.
Conformal fluctuations serve as a powerful tool to study the nature of quantum gravity. They lead, in a natural fashion, to the concept of stationary states for the quantum geometry. We attempt to incorporate the effect of conformal fluctuations into the background metric and matter. A modified set of equations, including the effect of conformal fluctuations, is presented and the solutions are discussed. It is shown that matter-free vacuum is unstable to conformal fluctuations. A scenario for creation of matter is indicated.
Spontaneous symmetry breaking in non inertial frames and curved spacetime
(Elsevier Science Publishers, 1982-05-03) Padmanabhan, T.
The conformally coupled Higgs scalar field (with λ φ4 quartic term) is studied in a class of non-lorentzian background metrics. It is shown that the spontaneous symmetry breaking depends crucially on the choice of the background metric. Various implications are discussed.
Can curvature effects be neglected in the early universe?
(Elsevier Science Publishers, 1982-05-31) Padmanabhan, T.; Vasanthi, M. M.
In the discussion of GUTS in the early universe it is assumed that there exists a locally inertial space-time region large enough to contain a sufficient number of particles justifying the use of fiat space statistical mechanics. We show that this assumption is false.
Quantum cosmology and stationary states
(Spinger, 1982-06-04) Padmanabhan, T.
A model for quantum gravity, in which the conformal part of the metric is quantized using the path integral formalism, is presented. Einstein's equations can be suitably modified to take into account the effects of quantum conformal fluctuations. A closed Friedman model can be described in terms of well-defined stationary states. The "ground states" sets a lower bound (at Plank length) to the scale factor preventing the collapse. A possible explanation for matter creation and quantum nature of matter is suggested.
General covariance, Accelerated frames and the particle concept
(Springer, 1982-09-11) Padmanabhan, T.
The definition of particle states in various accelerated frames is considered. It is shown that in any realistically accelerated system, quantum field theory can be formulated without any ambiguity. We further show that the definition of a particle based on Green's function techniques does not always agree with the definition based on explicit quantization. We analyse the standard accelerated detector results from this point of view and show that the uncertainty principle imposes a rigorous bound on these detection processes.
Conformal fluctuations in a quantum universe with a scalar field
(American Physical Society, 1982-10-15) Padmanabhan, T.
Quantum Conformal fluctuations are analyzed using the path integral approach. conformal fluctuations are introduced in a classical Robertson-Walkar universe with a massless scalar filed as a source. It is shown that the Conformal fluctuations diverge at the classical singularity. However the effective metric still retains the singularity. Some other aspects of introducing the scalar field in this quantum gravity model are briefly discussed.
Instability of flat space and origin of conformal fluctuations
(Elsevier Science Publishers, 1983-01-03) Padmanabhan, T.
It is shown that conformal fluctuations in the metric can be initiated by the vacuum fluctuations of a scalar field with mass greater than the Planck mass. Flatspace is unstable against such fluctuations.
Problems of singularity, particle horizon and flatness in quantum cosmology
(Elsevier Science Publishers, 1983-03-14) Narlikar, J. V.; Padmanabhan, T.
Classical relativistic cosmology is known to have the space-time singularity as an inevitable feature The standard big bang models have very small particle horizons in the early stages which make it difficult to understand the observed homogeneity in the universe. The relatively narrow range of the observed matter density in the neighbourhood of closure density requires highly fine tuning of the early universe. In this paper it is argued that these three problems can be satisfactorily resolved in quantum cosmology. It is shown that it is extremely unlikely that the universe evolved to the present state from quantum states with singularity and particle horizon. Similarly, it is shown that of all possible states the Robertson-Walker model of flat spatial sections is the most likely state for the universe to evolve out of a quantum fluctuation. To demonstrate these results a suitable formalism for quantum cosmology is first developed.
Quantum cosmology via path integrals
(Elsevier Science Publisher, 1983-05-01) Narlikar, J. V.; Padmanabhan, T.
The main purpose of this article is to report the progress of the path integral approach to quantum cosmology. Since quantum cosmology is an interdisciplinary field involving inputs from quantum theory, general relativity and cosmology, we begin with a brief survey of classical geometrodynamics and classical cosmology as well as an outline of the problems faced by any quantum theory of gravity. It is against this background that the authors’ approach described in sections 3—5 is to be viewed and assessed. The Feynman path integral formalism to the extent necessary for following this approach is described first in section 2. In section 3 it is shown that the limited goal of quantizing only the conformal part of the space-time metric can be reached with the help of path integral techniques. A case is made as to why this limited approach is still of relevance to quantum cosmology. Explicit examples are worked Out to show how meaningful conclusions can be drawn about quantum uncertainty at the classical singularity, the likelihood of singularity-free and horizon-free models in quantum cosmology and the limits on the validity of classical relativity close to the big bang. In section 4 the existence of stationary states of the universe is discussed. It is shown how the quantization of the conformal degree of freedom leads to stationary states for the quantum analogues of the classical models. The results are generalized and discussed in the framework of the superspace metric. The difficult problem of the back reaction of quantum conformal fluctuations on the space-time metric is tackled in a semiclassical fashion in section 5. In this approach the conformal part of the metric is treated classically while the conformal fluctuations are replaced by their expectation values. The resulting field equations are solved in a few simple cases and physically interpreted. This preliminary work holds promise for a more complete theory of the future. In the end a solution to the flatness problem of classical cosmology is suggested within the framework of conformal fluctuations.
Quantum gravity and the "flatness problem" of standard big bang cosmology
(Elsevier Science Publishers, 1983-06-13) Padmanabhan, T.
It is shown that, if the universe originated through quantum conformal fluctuations from the empty Minkowski space, then it is most likely to be spatially flat.
Quantum cosmology as a cure for three ailments of classical cosmology
(Astronomical Society of India, 1983-08-12) Narlikar, J. V.; Padmanabhan, T.
The standard big bang models of classical cosmology are known to possess three defects. The oldest known defect is spacetime singularity whose existence seems inevitable within the classical framework. The second defect is the existence of a particle horizon which severely limits communications across the distant parts of the universe whose observed homogeneity therefore becomes inexplicable. Recently a third defect has been highlighted, viz., the required fine tuning of the early universe close to the flat spatial model in order to account for the present range of its mean density. We show before that the injection of quantum ideas holds out hope of a cure for all the three ailments described above. Using a simple path integral formalism for quantum cosmology we present arguments which suggest that (i) it is extremely unlikely that the universe evolved to the present state from quantum states of singularity and particles horizon;(ii) of all the possible Robertson-Walker models that could evolve our of quantum fluctuations of the empty Minkowski universe the flat model is overwhelmingly probable.