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QCD Instantons and Inflation


In the first half of this dissertation, after giving a pedagogical introduction to quantum chromodynamics, we revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of a semiclassical calculation. For N_ f > N, a systematic computation is possible; for N_f < N, it is not. N_f = N is a borderline case. In our analysis, we see explicitly the exponential suppression of instanton effects at large N. As an application, we describe a test of QCD lattice gauge theory computations in the chiral limit.

For the second half, we turn our attention to inflation. Once again, a pedagogical overview of inflation is given, after which we explore some issues in slow roll inflation in situations where field excursions are small compared to M_p. We argue that for small field inflation, minimizing fine tuning requires low energy supersymmetry and a tightly constrained structure. Hybrid inflation is almost an inevitable outcome. The resulting theory can be described in terms of a supersymmetric low energy effective action and inflation completely characterized in terms of a small number of parameters. Demanding slow roll inflation significantly constrains these parameters. In this context, the generic level of fine tuning can be described as a function of the number of light fields, there is an upper bound on the scale of inflation, and an (almost) universal prediction for the spectral index. Models of this type need not suffer from a cosmological moduli problem.

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