Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-07-21
Class.Quant.Grav.19:515-526,2002
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages, Latex2e
Scientific paper
10.1088/0264-9381/19/3/307
Canonical quantization of an action containing curvature squared term requires introduction of an auxiliary variable. Boulware etal[1] prescribed a technique to choose such a variable, by taking derivative of an action with respect to the highest derivative of the field variable, present in the action.It has been shown that[2] this technique can even be applied in situations where introduction of auxiliary variables are not at all required, leading to wrong Wheeler-deWitt equation. It has also been pointed out that[2] Boulware etal's[1] prescription should be taken up only after removing all removable total derivative terms from the action. Once this is done only a unique description of quantum dynamics would emerge. For curvature squared term this technique yields, for the first time, a quantum mechanical probability interpretation of quantum cosmology, and an effective potential, whose extremization leads to Einstein's equation. We conclude that Einstein-Hilbert action should essentially be modified by at least a curvature squared term to get a quantum mechanical formulation of quantuum cosmology and hence extend our previous work[2] for such an action along with a scalar field.
Modak Bijan
Sanyal Abhik Kumar
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