Is Heat Death the only inevitable end? I have heard about heat death being the most probable end of the universe. But what are the other possible ends of the universe. I also came across a video stating that due to some effect called as "quantum tunelling" the universe could start again. But wouldnt that be a contradiction of the Second Law of thermodynamics?
 A: The discussion on the universe's death was addressed initially when physicist started using Einsteins' field equations (EFQ) to describe the whole universe. Once the cosmological principle was adopted, stating that at large scales the universe should be homogeneous and isotropic, one is led to the FLRW type of solutions for for EFQ. Within this solutions you can have an open, flat or closed universe. In the first case the universe would expand forever, in the second it will slow down its expansion for ever but won't ever stop, while in the last case, the universe would stop its expansion at some point and collapse back by means of the gravitational attraction. 
So an alternative, for the end of the universe, (back then) was this last scenario. Now the community currently believes after observations made on the expansion of the universe (and more over accelerated expansion) that our universe falls in the first case. It seems it will expand for ever driven by the so-called dark energy, meaning that energy will be just more and more diluted leading to the heat-death of the universe. 
Some other studies point perhaps to what you mentioned on tunnelling. When one studies the vacuum fluctuations from the point of view of quantum field theory in particular within the Standard Model framework, one finds that the behaviour of the Higgs field subject to a potential that suffers symmetry breaking can lead to the nucleation of bubbles of a different vacuum state. The original observations are due to Coleman in the 70s (See Fate of the False Vacuum I and Fate of the False Vacuum II). If it was the case that one of these bubbles is nucleated by tunnelling, anything consumed by this bubble would probably be turned into energy (the energy difference between its state and the new vacuum state) driving the expansion of the bubble as described in the papers. Current values of the parameters of the standard model point to the Higgs potential being metastable. There are also estimates on the decay rates of our false vacuum into true vacuum (see https://arxiv.org/abs/1707.08124).
