  The quantum cosmological wavefunction for a quadratic gravity theory derived
from the heterotic string effective action is obtained near the inflationary
epoch and during the initial Planck era. Neglecting derivatives with respect to
the scalar field, the wavefunction would satisfy a third-order differential
equation near the inflationary epoch which has a solution that is singular in
the scale factor limit $a(t)\to 0$. When scalar field derivatives are included,
a sixth-order differential equation is obtained for the wavefunction and the
solution by Mellin transform is regular in the $a\to 0$ limit. It follows that
inclusion of the scalar field in the quadratic gravity action is necessary for
consistency of the quantum cosmology of the theory at very early times.
