The quantum theory of a 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 $\Phi$. 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.

12 pages. Renormalizability properties of the action are clarified and a third-order differential equation for the wave function $\Psi$ with a dependence on the potential $V(\Phi )$ is included