Classical and Quantum Solutions and the Problem of Time in $R^2$ Cosmology

TL;DR

This paper explores classical and quantum solutions in $R^2$ cosmology, providing exact solutions and analyzing the problem of time in general relativity through these models.

Contribution

It presents the first exact classical and quantum solutions in pure $R^2$ cosmology and examines the problem of time within this framework.

Findings

Exact classical solutions in pure $R^2$ cosmology

Exact quantum solutions to the Wheeler-DeWitt equation in this setting

Insights into the problem of time in general relativity

Abstract

We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology exactly. Comparing these classical and quantum solutions in $R^2$\ cosmology, we have studied the problem of time in general relativity.