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.
Categories: gr-qc