Quantum conformal fluctuations revisited
The conformal quantization method of Narlikar and Padmanabhan is reformulated with a view to take into account theexact propagator and to provide explicitnumerical estimates of various predictions for dust cosmologies. It is found that in spite of the divergence of quantum fluctuations at the big-bang epoch it is possible to construct wave packets which remain sharp fromt=10−70s, say, up to the present epoch provided the present state is finely tuned to the classical one. Also, if the transition probability from the Minkowski to the FRW metric is calculated using Gaussian wave functions (with zero mean) then thet2/3 models withk = 0, ± 1 cannot be distinguished, i.e., a fine tuning to the flat (k=0) model does not seem to result if the conformal factor depends on time only.
KeywordsDust Wave Function Present State Wave Packet Differential Geometry
Unable to display preview. Download preview PDF.
- 1.Isham, C. J., Penrose, R., and Sciama, D. W. (1975).Quantum Gravity (Clarendon Press, Oxford).Google Scholar
- 2.Guth, A. H. (1981).Phys. Rev. D,23, 347.Google Scholar
- 3.Padmanabhan, T. (1982). Ph.D. Dissertation, Tata Institute of Fundamental Research, India.Google Scholar
- 4.Narlikar, J. V. (1981).Found. Phys.,11, 473.Google Scholar
- 5.Narlikar, J. V., and Padmanabhan, T. (1983).Ann. Phys.,150 (2), 289.Google Scholar
- 6.Narlikar, J. V., and Padmanabhan, T. (1983).Phys. Rep.,100 (3), 151.Google Scholar
- 7.Narlikar, J. V. (1978).Lectures on General Relativity and Cosmology (Macmillan, New York).Google Scholar
- 8.Infeld, L., and Schild, A. (1945).Phys. Rev.,68, 250.Google Scholar
- 9.Schiff, L. I. (1986).Quantum Mechanics (McGraw-Hill, New York).Google Scholar