Research Publications

Now showing 1 - 10 of 25

Complex effective path: A semi-classical probe of quantum effects
(American Astronomical Society, 2012-01-23) Singh, Suprit; Padmanabhan, T.
We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the effective path will also, in general, be complex. The imaginary part of the effective action is known to be related to the probability of particle creation by an external source and hence we expect the imaginary part of the effective path also to contain information about particle creation. We try to identify such features using simple examples including that of an effective path through the black hole horizon leading to thermal radiation. Implications of this approach are discussed.
Quantum cosmology and the early universe
(Italian Physical Society, 1985-11-15) Narlikar, J. V.
The classical Friedmann cosmology is known to suffer from three major conceptual problems :' (i) spacetime singularity; (ii) particle horizons and (iii) flatness. It is shown that these problems may be resolved during the quantum era of the early universe. Recent attempts in this direction based on the quantization of the conformal degrees of freedom are reviewed here.
Big bang and quantum cosmology
(-, 1985-09-05) Narlikar, J. V.
Quantum fluctuations near the classical spacetime singularity
(World Scientific, 1984-01-18) Narlikar, J. V.
New approach to quantum cosmology
(World Scientific, 1984-10-29) Narlikar, J. V.
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.
Stationary states in quantum cosmology
(Institute of Mathematics and its Application, 1983-07-29) Narlikar, J. V.
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.
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.
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.

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