Initial conditions for perturbations in R+εR^2 cosmology

Abstract

In a classical inflationary cosmology based on the R+εR2 Lagrangian the parameters of the model (such as ε and the initial conditions for inflationary trajectories) are constrained by the observational requirement that any perturbations be delivered small to the present horizon volume. Previous calculations of the evolution of these perturbations (and, hence, of the parameter constraints enforced by their evolution) have assumed that the modes begin in their ground state. In this paper, following the procedure of Halliwell and Hawking, the Wheeler-DeWitt equation is derived for this model’s inhomogeneous modes in perturbative superspace. Then, the two boundary-condition proposals of Hartle and Hawking ("no boundary") and Vilenkin ("tunneling from nothing") are implemented, verifying that both boundary conditions require the inhomogeneous modes to begin in their ground states.