Simplicial minisuperspace models in the presence of a massive scalar fieldwith arbitrary scalar coupling eta R phi(2)

We consider a simplicial minisuperspace model based on a cone over the alph a(4) triangulation of the 3-sphere, in the presence of a massive scalar fie ld, phi, with arbitrary scalar coupling term eta R phi(2). By restricting a ll the interior edge lengths and all the boundary edge lengths to be equiva lent and the scalar field to be homogeneous on the 3-space, we obtain a two -dimensional minisuperspace model {s(i), phi(i)} for what is one of the mos t relevant triangulations of the spatial universe. We solve the two classic al equations and find that there are both real Euclidean and Lorentzian cla ssical solutions for any size of the boundary 3-space, alpha(4). After stud ying the analytic properties of the action in the space of complex edge len gths we then obtain steepest descents contours of constant imaginary action passing through Lorentzian classical geometries giving the dominant contri bution and yielding a convergent wavefunction of the universe. We also show that the semi-classical wavefunctions for the Euclidean solutions associat ed with large boundary 3-spaces are exponentially suppressed.