Research Papers (JVN)
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Item Quantum cosmology via path integrals(Elsevier Science Publishers, 1983-05-05) 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 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 Quantum conformal fluctuations in a singular spacetime(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 singularities. 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 meaningless. 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.Item Quantum fluctuations in the conformally flat and the Schwarzschild spacetimes(Springer, 1981-01-12) 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 Schwarzschild spacetime. 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 Schwarzschild metric are, however, damped at the event horizon. Similar conclusions are drawn about the Reissner-Nordstrom space-time.Item Quantum fluctuations in the Schwarzschild spacetime(-, 1980-01-01) Narlikar, J. V.; Padmanabhan, T.