Steepest descent contour analysis of quantum cosmology in two-dimensional dilaton gravity theories

In this work we study quantum cosmology in the context of two-dimensional dilation gravity theories. Euclidean functional integrals are used to describe the wave function of the model two-dimensional universe. We show that, as in the four-dimensional case, the Euclidean action is not bounded from below. The functional integrals are studies following the general method of Halliwell and Louko which calls for the use of complex contours. The method of steepest descent is used to evaluate the lapse integral while the remaining functional integrals are evaluated exactly. The propagation amplitude is calculated in the limit of large final scale factor describing a region near the end of superspace