Research Papers (JVN)
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Item Conformal quantization and space-time singularity(World Scientific Publishing group, 1986-06-06) Joshi, P. S.; Narlikar, J. V.This work generalizes earlier results of conformal quantization that within the full range of space-times conformal to any singular space-time satisfying Einstein's field equations for minimally coupled matter, the singular solutions form a set of zero-probability measure. A wider definition of space-time singularity that includes the curvature singularity assumed in the earlier work (op. cit.) is adapted and it is shown that the previous conclusion stands even when the present state of the universe is defined by wave functionals that are not necessarily wave packets. Within the present framework of quantum gravity therefore it seems extremely unlikely that the universe had a singular origin.Item Creation field cosmology : A possible solution to singularity, horizon and flatness problems(American Physical Society, 1985-10-15) Narlikar, J. V.; Padmanabhan, T.A solution of Einstein s equations which admits radiation and a negative-energy massless scalar creation field as a source is presented. It is shown that the cosmological model based on this solu- tion satisfies all the observational tests and thus is a viable alternative to the standard big-bang model. The present model is free from singularity and particle horizon and provides a natural ex- planation for the flatness problem. We argue that these features make the creation-field cosmologi- cal model theoretically superior to the big-bang model.Item Quantum fluctuations near the classical spacetime singularity(World Scientific, 1984-01-18) Narlikar, J. V.Item Vanishing likelihood of spacetime singularity in quantum conformal cosmology(Springer, 1984-01-06) Narlikar, J. V.A general formalism is developed for studying the behavior of quant&ed conformal fluctuations near the space-time singularity of classical relativistic cosmology. It is shown that if the material contents of space-time are made of massive particles which obey the principle of asymptotic freedom and interact only gravitationally, then it is possible to estimate the quantum mechanical probability that, of the various possible conformal transforms of the classical Einstein solution, the actual model had a singularity in the past. This probability turns out to be vanishingly small, thus indicating that within the regime of quantum conformal cosmology it is extremely unlikely that the universe originated out of a space-time singularity.Item Quantum cosmology as a cure of three ailments of classical cosmology(Astronomical Society of India, 1983-08-12) Padmanabhan, T.; Narlikar, J. V.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.Item 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 difTicult 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.Item Elimination of the standard big bang singularity and particle horizon through quantum conformal fluctuations(Elsevier Science Publishers, 1983-04-13) Narlikar, J. V.It is shown that within the framework of quantum conformal fluctuations it is extremely unlikely that the universe originated from a state of singularity and small particle horizon.Item Quantum fluctuations near the classical space-time singularity(Springer, 1979-01-03) Narlikar, J. V.The method of path integration is used to study the effects of quantum fluctuations in the space-time geometry near the classical singularity of general relativity. It is shown that in certain special cases explicit Feynman propagators can be constructed which enable us to evaluate these fluctuations quantitatively. The cases discussed are (i) the gravitational col- lapse of a uniform dust ball, (ii) the Friedmann cosmologies, (iii) the axisymmetric Bianchi type I cosmological model, and (iv) the general anisotropic Bianchi type I cosmological model. In all cases discussed here the quantum uncertainty grows to infinity as the classical space-time singularity is approached. In this wider regime of quantum gravitation non- singular solutions can occur with finite probabilities.Item Quantum fluctuations near the classical space-time singularity(Springer, 1978-04-03) Narlikar, J. V.The method of path integration is used to study the effects of quantum fluctuations in the space-time geometry near the classical singularity of general relativity. It is shown that in certain special cases explicit Feynman propagators can be constructed which enable us to evaluate these fluctuations quantitatively. The cases discussed are (i) the gravitational col- lapse of a uniform dust ball, (ii) the Friedmann cosmologies, (iii) the axisymmetric Bianchi type I cosmological model, and (iv) the general anisotropic Bianchi type I cosmological model. In all cases discussed here the quantum uncertainty grows to infinity as the classical space-time singularity is approached. In this wider regime of quantum gravitation non- singular solutions can occur with finite probabilities.Item Quantum fluctuations in gravitational collapse and cosmology(Will-Blackwell, 1978-01-22) Narlikar, J. V.It is shown that the conformal degrees of freedom in the metric tensor can be quantized and that this procedure leads to fluctuations around the solutions of the classical Einstein field equations. These fluctuations become progressively more important as the classical solution approaches the space-time singularity. An explicit calculation is given of the quantum mechanical propagator which describes the conformal fluctuations in a collapsing homogeneous ball of dust. As the state of classical singularity is approached the quantum uncertainty diverges. Within the range of quantum uncertainty non-singular final states are possible. The solution can also be applied to the Friedmann models with the conclusion that the Universe need not have originated in a unique classical big bang. Non-singular models or models without particle horizons are permitted within the range of the quantum uncertainty.