Energy is conserved - it cannot be created or destroyed, so the amount of energy in the universe is constant and has always been constant. The level of energy of the universe must have been determined before or during the big bang.
So if E=mc^2 and energy and mass are two forms of the same thing, then the universe can only attain a certain mass until all the energy in the universe has been expended, at which point it would stop expanding.
Am I correct?