# Quantum cosmology of quadratic f(R) theories with a FRW metric

## TL;DR

This paper investigates the quantum cosmology of quadratic f(R) gravity with a FRW metric, solving the classical and quantum equations numerically to explore inflation scenarios and wave function properties.

## Contribution

It provides a numerical analysis of the Wheeler-DeWitt equation in quadratic f(R) theories, highlighting the impact of boundary conditions on the universe's wave function.

## Key findings

- Wave function can be normalizable with appropriate boundary conditions
- Two inflation scenarios are identified: inflation with exit and inflation alone
- Numerical solutions depend strongly on boundary condition choices

## Abstract

We study the quantum cosmology of a quadratic $f(R)$ theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamics of the scalar field is induced. The classical equations of motion and the Weeler-deWitt equation, in their exact versions, are solved numerically. From the choice of a free parameter in the action follow two cases, inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe seems to be normalizable and consistent with hermitian operators.