Quantum Cosmology for a Quadratic Theory of Gravity

TL;DR

This paper solves the Wheeler-DeWitt equation exactly for a quadratic gravity model in quantum cosmology, demonstrating boundary conditions that align with Vilenkin's proposals for the wave function of the universe.

Contribution

It provides an exact solution to the Wheeler-DeWitt equation in a pure $R^2$ quantum cosmology model, advancing understanding of boundary conditions in quantum gravity.

Findings

Wave functions vanish at the origin, consistent with Vilenkin's boundary condition.

Exact solutions are obtained for the closed homogeneous and isotropic universe.

Supports the Vilenkin proposal for the wave function boundary condition in quadratic gravity.

Abstract

For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin of the universe the wave functions behave as suggested by Vilenkin.