orion1977 said:
If the universe is eternal, then why has it not reach heat death by now?
There are at least two ways of responding to this that I'm aware of:
(1) An eternal universe does not have to reach and then remain stuck in the same state. The classical version of this is that the universe we observe is a random fluctuation from an overall "heat death" thermal equilibrium state in a localized region. The quantum version of this is a theory like eternal inflation, in which the eternal "background" is a state that continually generates new observable universes, including ours, by means of phase transitions in an underlying quantum field.
(2) An eternal universe might not have a state of maximum possible entropy, which is what "heat death" requires. For example, our best current model of our observable universe is that it is spatially infinite and will keep expanding forever. If this is correct, then the entropy of the universe has no maximum--there is no finite upper bound. So entropy can continue increasing forever without ever reaching a "heat death" state.
However, both of these answers have the universe, or at least our observable universe, having a finite extent in the
past -- a finite past time before which there was something quite different (or possibly nothing at all, depending on which speculative model you want to discuss). So they don't really say anything about
why "an infinite past time" is or is not possible. That's because we know from actual observations that, at the very least, there was a finite past time at which what is now our observable universe was in a very different state, so any model which has something similar to our current universe existing for infinite past time is ruled out by the data.