Quantum cosmology with a curvature squared action

TL;DR

This paper develops a quantum cosmological model with a curvature squared term, deriving the Wheeler-DeWitt equation, probability densities, and showing consistency with classical Einstein equations in the weak energy limit.

Contribution

It introduces a canonical formulation for curvature squared actions in quantum cosmology, leading to new solutions of the wave equation and insights into quantum-classical correspondence.

Findings

Derived the Wheeler-DeWitt equation for curvature squared gravity

Obtained probability and current densities from the wave function

Showed classical Einstein equations emerge in the weak energy limit

Abstract

The correct quantum description for a curvature squared term in the action can be obtained by casting the action in the canonical form with the introduction of a variable which is the negative of the first derivative of the field variable appearing in the action, only after removing the total derivative terms from the action. We present the Wheeler-DeWitt equation and obtain the expression for the probability density and current density from the equation of continuity. Furthermore, in the weak energy limit we obtain the classical Einstein equation. Finally we present a solution of the wave equation.