UBC Theses and Dissertations
Birth of universes with non-minimal coupling Fakir, Redouane
Part I : 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 λ of the inflaton 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 ξ is set to zero). It is shown here that in the more general case of non-minimal coupling (ξ≠0 ), 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 ξ 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. Part II : The possibility of inflation during induced gravity spontaneous symmetry breaking with Zee's Lagrangian L — ξφ²R/2 –δ[sub α]φδ[sup α]φ/2-λ(φ²-v²)² 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 'chaotic' version, which is very similar to the model discribed in Part I, proves to be more attractive in most respects. In particular, the belief that λ has to be excessively small is shown to be well founded only for 'ordinary' inflation. Part III : The minisuperspace canonical quantization is applied to the λφ⁴ theory of Part I, 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 Hartle and Hawking's wave functions are preserved in non-minimal coupling. The results also apply to the quartic induced gravity potential of Part II. It is noted that the minisuperspace wave function can be regarded, not as the wave function of the Universe, but rather as describing an ensemble of inflationary sub-universes. Predictions of classical initial conditions could then be made using an ordinary frequency interpretation of quantum probabilities.
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