Research Papers (TP)
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Item Mach's principle and the notion of time(Indian Academy of Sciences, 2009-09-12) Padmanabhan, T.The role of time coordinate in the realization of March's principles is highlighted. It is shown that Mach's principle is linked to the definition of a 'particle'. These results a deep connection between quantum gravity an Mach's principle.Item 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.Item 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.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 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.Item Notes on Semiclassical Gravity(Elsevier Science Publishers, 1989-07-06) Singh, T. P.; Padmanabhan, T.In this paper we investigate the different possible ways of defining the semiclassical limit of quantum general relativity. We discuss the conditions under which the expectation value of the energy-momentum tensor can act as the source for a semiclassical, c-number, gravitational field. The basic issues can be understood from the study of the semiclassical limit of a toy model, consisting of two interacting particles, which mimics the essential properties of quantum general relativity. We define and study the WKB semiclassical approximation and the gaussian semiclassical approximation for this model. We develop rules for finding the back-reaction of the quantum mode 4 on the classical mode Q. We argue that the back-reaction can be found using the phase of the wave-function which describes the dynamics of 4. We find that this back-reaction is obtainable from the expectation value of the hamiltonian if the dispersion in this phase can be neglected. These results on the back-reaction are generalised to the semiclassical limit of the Wheeler-Dewitt equation. We conclude that the back reaction in semiclassical gravity is ( Tlk) only when the dispersion in the phase of the matter wave functional can be neglected. This conclusion is highlighted with a minisuperspace example of a massless scalar field in a Robertson-Walker universe. We use the semiclassical theory to show that the minisuperspace approximation in quantum cosmology is valid only if the production of gravitons is negligible.