Observational test of quantum cosmology

We compute the tensor CMB anisotropy power spectrum for singular and non-singular instantons describing the beginning of an open universe according to the Euclidean no boundary proposal. Singular instantons occur generically, whereas non-singular instantons require more contrived scalar field potentials. For the latter, we consider potentials in which a sharp feature, either negative or positive, is added to a gently sloping potential. In the first case one finds a nearly divergent contribution to the low multipole CMB anisotropy, in conflict with the COBE observations. In the second case the divergence is weaker, but matching the low multipoles forces the added feature to be large and narrow. For singular instantons, there is a better match to the observations, without any such contrivance. The distinction between singular and nonsingular instantons disappears in the limit as the universe becomes flat, but is still observable for densities as high as 0.7 of the critical density.