Letter: The Quantum Theory of the Quadratic Gravity Action for Heterotic Strings

Abstract

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