The quantum theory of a quadratic gravity action for heterotic strings

TL;DR

This paper derives the wave function for a quadratic gravity theory from heterotic string effective action, analyzing quantum cosmology predictions and the quantum-classical transition in minisuperspace variables.

Contribution

It provides a first-order quantum wave function solution for heterotic string-derived quadratic gravity and examines quantum effects on inflationary dynamics.

Findings

Predictions for inflation remain valid in this quantum framework.

Quantum corrections cause shifts from classical solutions at third order.

Formal expressions for average paths in minisuperspace are derived.

Abstract

The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in ${{e^{-\Phi}}\over {g_4^2}}$ by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the potential is slowly varying with respect to $\Phi$. Predictions for inflation based on the solution to the second-order Wheeler-DeWitt equation continue to hold for this theory. It is shown how formal expressions for the average paths in minisuperspace $\{< a(t) >, < \Phi(t)> \}$ determine the shifts from the classical solutions to $a_{cl}(t)$ and $\Phi_{cl}(t)$, which occur only at third order in the expansion of the integrals representing the expectation values.