QUANTUM CREATION OF UNIVERSES WITH NONMINIMAL COUPLING

The minisuperspace canonical quantization is applied to a 4 theory where the usual assumption of minimal coupling between the curvature and the scalar field is dropped. Different sets of variables are used and special attention is paid to the invariance of the quantization procedure and to the related issue of factor ordering in the Wheeler-DeWitt equation. It is shown that the generic features of Vilenkin's and the Hartle-Hawking wave functions are preserved in nonminimal coupling. The results also apply to the quartic induced-gravity potential. It is noted that the minisuperspace wave function could be regarded not as the wave function of the Universe, but rather as describing an ensemble of inflationary subuniverses. Predictions of classical initial conditions could then be made using an ordinary frequency interpretation of quantum probabilities. © 1990 The American Physical Society.