This question can't be answered. Why?
Because it's a philosophy, mathematical, physics and thermodynamic related.
Firstly, thermodynamics dictates the universe should have a finite amount of energy because of the arrow of time and how time is same for everyone and entropy.
However; physics dictates time isn't constant. It can speed up, slow down and even appear to stand still (In a black-hole). So we have conflict there.
Mathematics shows the universe should be either expanding; but physics show that gravity should mean the universe should be constant or at least the rate of expansion has to be slowing down but it isn't; its accelerating if anything..
Philosophy will simply say something similar about what we mean when we say infinite.
So we don''t know for sure, this can't be tested either, well not right now anyway. We don't know much about dark energy so yeh.