However, the unproven nature of the relationship between actual physical time and imaginary time incorporated into such models has raised criticisms. Roger Penrose has noted that there needs to be a transition from the Riemannian metric (often referred to as " Euclidean " in this context) with imaginary time at the Big Bang to a Lorentzian metric with real time for the evolving Universe. Also, modern observations suggest that the Universe is open and will never shrink back to a Big Crunch. If this proves true, then the end-of-time boundary still remains.