QUANTUM COSMOLOGY AND THE VALUE OF A

We analyze a simple quantum cosmological model with just a Lambda term present. Different results for the expected value of Lambda are obtai ned depending on the boundary conditions applied. In the Euclidean reg ime the Hartle-Hawking boundary condition gives the factor exp(1/Lambd a) but, in agreement with Rubakov et al.,(10) is badly behaved for neg ative Lambda. Tunneling boundary conditions suggest an initially large value for Lambda. If only Lorentzian regions are considered, all boun dary conditions suggest an initially large value of Lambda for spatial curvature k = 1. This differs from the previously obtained results of Strominger(11) for such models, who implicitly assumed that the unive rse has occurred in its present (large size) form by a quantum event. Whereas, quantum behavior should be restricted to epochs when the univ erse was similar to Planck size.