Quantifying the Degree of Fine-tuning in Models of Inflation

Abstract

Although in ationary theory is a simple and elegant solution to the horizon and at- ness problems, as the eld has developed, in ationary models have greatly increased in complexity and degree of ne-tuning. My thesis works to take these often vague notions of complexity and ne-tuning and de ne speci c measures for determining the degree of ne-tuning in an in ationary model. Since recent observations have favored large eld plateau potentials (hereafter \plateau potentials"), the main body of my project ex- plores a new method of examining the ne-tuning in such models. Our method is based on the idea that plateau models are ne-tuned because the series expansion of their potentials contain an in nite number of non-zero terms that must be precisely balanced to create a plateau. We nd that perturbing a plateau potential with a monomial in the eld causes signi cant drift in the ns-r plane. A large enough perturbation amplitude causes convergence on the ns-r values for the perturbing function. This is a signi cant concern when it comes to constraining large eld plateau models. Adding a mono- mial perturbation has the e ect of grafting a steep slope onto the plateau. However, Mukhanov (2014) used exactly this idea to propose a solution to the multiverse problem. We applied our ns-r drift methodology to Mukhanov's model and found that in order to solve the multiverse problem one of his two proposed models must undergo enough drift to push its predictions outside of Planck Collaboration et al. (2015) constraints. As theorists continue to construct new models of in ation, it will be important to keep in mind the instabilities inherent in plateau potentials. If this and other manifestations of ne-tuning continue to plague in ationary theory, it might even be advisable to extend one's outlook to other theories of the early universe, such as eckpyrotic or cyclic models. Further work in exploring the existence/amount of ne-tuning in such non-in ationary theories is recommended to compliment the work done on the subject within inflationary theory.