Wave function of the Universe as a leaking system

We propose a path-integral formulation for the wave function of the Universe which requires neither the Euclidean nor the conformal rotation. The boundary condition is taken to be that ‘‘all possible boundaries are included.’’ The resulting wave function in a simple model is shown to have the following properties: (i) the wave function tends to zero as the scale factor of the Universe tends to zero; (ii) in the semiclassical regime, it contains only the expanding component; (iii) it favors inflation.