This thesis presents the study of a model cosmology based on the R +ɛR² gravitational Lagrangian. It may be roughly divided into two distinct parts. First, the classical inflationary scenario is developed. Then, the formalism of quantum cosmology is employed to determine initial conditions for the classical model.
In the work on the classical model, the evolution equations for an isotropic and homogeneous universe are solved to exhibit both early-time inflation and a smooth transition to subsequent radiation-dominated behavior. Then perturbations on this isotropic background are evolved through the model to provide constraints on the model parameters from the observational limits on anisotropy today. This study concludes that such an inflationary model will prove a viable description for our universe if the initial Hubble parameter Hi is bounded from below, Hi > 10⁻⁵ lPl⁻¹, and if ɛ > 10¹¹ lPl².
In the work on the wave function, the two boundary conditions of Vilenkin ("tunneling from nothing") and Hartle and Hawking ("no boundary") are compared. The wave functions obtained are restricted to the initial edge of classical Lorentzian inflationary trajectories as distributions over initial conditions for the classical inflationary model. It is found that Vilenkin's wave function prefers the universe to undergo a great deal of inflation, whereas Hartle and Hawking's wave function prefers the universe to undergo little inflation. Finally, both boundary conditions are shown to require that inhomogeneous perturbative modes start out in their ground states.
