DOES QUANTUM MECHANICS INDICATE AN ETERNAL UNIVERSE

If you have a universe that obeys the conventional rules of quantum mechanics, has a non-zero energy, and the individual laws of physics are themselves not changing with time, that universe is necessarily eternal. The time parameters in Schrodinger's equation, telling you how the universe evolves, goes from minus infinity to infinity. Now this might not be the definitive answer to the real world because you could always violate the assumptions of the theory, but because it takes quantum mechanics seriously it's a much more likely a starting point for analyzing the history of the universe. Assuming the validity of the Schrodinger equation has a deep, if somewhat obvious consequence, time stretches for all eternity. In quantum mechanics unitary evolution ensures that there is no boundary to time. The variable 't' runs from -00 to +00 just implies that quantum time evolution is information-preserving. We can extrapolate from the present indefinitely into the past or future. This allows us to describe a moment prior to a given moment if there is such a moment.
A competing scenario from quantum cosmologists talks about the creation of the universe from nothing. In this hypothesis there is literally a moment in the history of the universe prior to which there weren't any moments. There is a boundary of time (presumably at the Big Bang), prior to which there was nothing. No matter, not even a quantum wave function; there was no prior thing, because there was no sensible notion of prior. Accordingly time enters into existence when you measure duration and numerical order of motion into space. It is not time that is relative but the speed of material change.