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We consider two kinds of higher dimensional models which upon dimensionalreduction lead to Jordan-Brans-Dicke type effective actions in four dimensionswith the scale factor of the extra dimensions playing the role of the JBDfield. These models are characterized by the potential for the JBD field whicharises from the process of dimensional reduction, and by the coupling of theinflaton sector with the JBD field in the Jordan frame. Taking into account thefact that these models allow the possibility of enough inflation and dynamicalcompactification of the extra dimensions, we examine in the context of thesemodels the other conditions which need to be satisfied for a viable scenario ofextended inflation. We find that the requirements of conforming to generalrelativity at the present epoch, and producing suitable bubble spectrums duringinflation lead to constraints on the allowed values taken by the parameters ofthese models. A model with a ten dimensional JBD field is able to satisfy thecondition for appropriate density perturbations viewed in the conformalEinstein frame, with a stringent restriction on the initial value taken by thescale factor of the extra dimensions.Comment: 17 pages, 2 Postscript figures, To appear in Physical Review

Constraints on higher dimensional models for viable extended inflation