Quantum Cosmology in Scalar-Tensor Theories With Non Minimal Coupling

TL;DR

This paper develops a method to solve the Wheeler-DeWitt equation in non-minimal scalar-tensor quantum cosmology by using conformal transformations, enabling analysis of classical limits in different frames.

Contribution

It introduces a conformal transformation approach to convert non-separable quantum equations into integrable forms, facilitating solutions and classical limit analysis in scalar-tensor theories.

Findings

Classical limit occurs at small scale factors in Einstein's frame.

Classical limit occurs at small scalar field values in Jordan's frame.

Method allows construction of solutions in original frames from known minimal coupling solutions.

Abstract

Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form, which corresponds to the minimal coupling case, whose general solution is known. Performing the inverse conformal transformation in the solution so found, we can construct the corresponding one in the original frame. This procedure can also be employed with the bohmian trajectories. In this way, we can study the classical limit of some solutions of this quantum model. While the classical limit of these solutions occurs for small scale factors in the Einstein's frame, it happens for small values of the scalar field non minimally coupled to gravity in the Jordan's frame, which includes large scale factors.