Mathematics – Logic
Scientific paper
Mar 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phdt.........9f&link_type=abstract
Ph.D. Thesis British Columbia Univ., Vancouver.
Mathematics
Logic
1
Astronomical Models, Big Bang Cosmology, Coupling, Universe, Curvature, Expansion
Scientific paper
Models of cosmological inflation are plagued with a severe and seemingly unavoidable problem: in order to produce density perturbations of an amplitude consistent with large-scale observations, the self-coupling lambda of the inflation field has to be tuned to an excessively small value. In all these models, however, the scalar field is taken to be minimally coupled to the scalar curvature (the curvature coupling theta is set to zero). It is shown that in the more general case of non-minimal coupling (theta does not equal zero), and within the framework of Linde's chaotic inflation, the constraint on the self-coupling can be relaxed by several orders of magnitude. This stems essentially from the fact that, contrary to common belief, the curvature coupling theta can be almost arbitrarily large without upsetting the inflationary scenario. Non-minimal coupling may thus provide a relatively simple solution to the long-standing problem of excessive density perturbations in inflationary models. The possibility of inflation during induced gravity spontaneous symmetry breaking with Zee's Lagrangian is confirmed. The ordinary and chaotic versions of this model are compared and found to differ substantially regarding the constraints on initial conditions and field parameters. The minisuperspace canonical quantization is applied, where the usual assumption of minimal coupling between the curvature and the scalar field is dropped. It is shown that the generic features of Vilenkin's, and Hartle and Hawking's wave functions are preserved in non-minimal coupling.
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