If we assumed that the big bang hypothesis is true, then the universe is in cooling and expanding phase, and this is justified by the star spectrum analysis. What about the entropy variation of universe? I think that It is decreasing according to Boltzmann theory.
Now, if we consider that the universe is an isolated system (we don't know and we can't define what can be the external medium to universe), its entropy is increasing (there is no exchange of entropy and the universe evolution is not reversible) because of entropy generation