Prospects in Extended Inflation

This work explores the various aspects in making a successful model of extended inflation, which should solve all the problems of the Standard Cosmology without creating new ones. Extended inflationary models are based on Brans -Dicke like theories. In the extended inflationary scenario, inflation occurs when the inflation field is trapped in a false vacuum and ends via the nucleation and percolation of true vacuum bubbles. We study the nucleation probability of these true vacuum bubbles. We find that in the context of extended inflation, the nucleation rate can have very strong time dependence through the time dependence of the Brans-Dicke like field; this can have a pronounced effect on the percolation of true vacuum bubbles. Physical constraints on generalized extended inflationary models are derived. We find that there are sizable portions in the parameter spaces of these theories that allow for good extended inflation. Two examples of Brans-Dicke like theories are given. First example involves allowing that the Brans-Dicke field may couple differently to dark matter than to normal matter. It has satisfactory extended inflation. The second example arises from the dimensional reduction of higher-dimensional Kaluza-Klein theories, and gives unexpected results. The effects of higher-order curvature terms on extended inflation are also examined. We find that there must be an upper limit on the coupling strength of these terms, if they are not to spoil the good features of extended inflation. Lastly, we present a model which makes use of the non-linear realization of scale-invariance, with the dilaton coupled to the usual inflation potential. We find that extended inflation can occur successfully in this model. Further, it is quite natural for a second period of slow-roll inflation to follow. The combination of these two inflationary periods can result in exciting possibilities for structure formation. The viability of extended inflationary models and the richness of physics they contain indicate that extended inflation is a promising way to implement inflation.