# Induced Gravity and Quantum Cosmology

## TL;DR

This paper explores the quantum cosmology of induced gravity models using the Wheeler-DeWitt equation, finding exact solutions for power-law scalar potentials and establishing a classical-quantum correspondence.

## Contribution

It provides exact quantum solutions for a class of induced gravity models with power-law potentials, extending classical solutions into the quantum regime.

## Key findings

- Exact solutions to the Wheeler-DeWitt equation for induced gravity models.
- Establishment of a classical-quantum correspondence in these models.
- Potential relevance to inflationary cosmology during the early universe.

## Abstract

We study the Wheeler-DeWitt equation for a class of induced gravity models in the minisuperspace approximation. In such models a scalar field nonminimally coupled to gravity determines the effective Newton's constant. For simplicity our analysis is limited to power-law potentials for the scalar field which have exact classical solutions. We show that these models have exact solutions also when quantised. Finally the Einstein Frame form of these solutions is obtained and a classical-quantum correspondence is found. Realistic induced gravity models also must include a symmetry breaking term which is needed in order to obtain a gravitational constant, successful inflation and a subsequent standard cosmological evolution. Nonetheless the potentials considered are important as they may describe the inflationary phase when the symmetry breaking part of the potential is negligible.