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The quantum theory of a quadratic gravity action for heterotic strings

Simon Davis·Hugh Luckock
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Abstract

The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in ${e^{-Φ}\over {g_4^2}}$ 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 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 $\{< a(t) >, < Φ(t)> \}$ determine the shifts from the classical solutions to $a_{cl}(t)$ and $Φ_{cl}(t)$, which occur only at third order in the expansion of the integrals representing the expectation values.

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Simon Davis, Hugh Luckock. 2002-02-13. The quantum theory of a quadratic gravity action for heterotic strings. https://arxiv.org/abs/gr-qc/0201002

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