Applying entropy to the Big Bang model has always sounded controversial to me.
For the Big Bang theory we consider "universe" what is occupied by matter and not an empty container of infinite dimensions in which matter expands. If so, the laws of physics would be violated and we could not use them: the parts of the universe furthest from us, in fact, continue to move away, in acceleration, at higher speeds than the light.
Rather than accepting a "universe metric" that does not follow the laws of physics, I prefer the idea that there are other dimensions in which the universe, without a center, is in fact the surface of a hypersphere, in continuous growth. Here the laws of known physics, with a large mortgage on thermodynamics too, could no longer apply.
Entropy in fact faces unsolved issues too: entropy could not decrease from the early universe, where matter and energy were uniformly distributed, to our one, in which nothing is uniform. Its function then also depends from the expansion of the universe, as for a gas expanding in an adiabatic but irreversible transformation.
So, either we look for a model in which the metric of the universe is not what appears to us (but it’s only the result of our perception of an existing fourth spatial dimension), or we must accept the idea that physics should only be applied to the nearest portion of universe.
If this were the case, outside of this close portion, the laws we know do not apply anymore.
This is really too much and I want to go beyond with a crazy idea:
By accepting the idea of a fourth dimension, as in a sort of differential geometry, one would consider a coordinate transformation for a three-dimensional observer who studies a four-dimensional universe. This transformation would apply to the laws of our physics and then to the whole theory.
The way chosen to set the problem is very rudimentary.
For simplicity, we can think to an observer who can move in one dimension along the circumference of a circle: that is the universe he perceives. The real universe is instead in two dimensions represented by an annulus of the previous circle.
Through the whole annulus, the laws of physics apply. For example, objects can move only at a speed lower than light.
Now suppose that a point inside the annulus is perceived by the observer as its projection from the center on the circumference.
The velocity v of a distant point, which leaves the circumference approaching the center, would be perceived by the observer as v1 that could be greater than light. Note that this effect would not be perceived for points close to the observer.
Let’s apply now this idea to our universe, which lies on the surface of a hypersphere whose radius is continuously growing. We cannot observe recent galaxies if these are far away, as their rays of light haven’t reached us yet. We can instead observe images of the older ones that, born closer to the center, lay projected onto the surface. Speeds higher than light are possible but here nothing is moving: is the hypersphere growing.
We cannot directly observe the fourth spatial dimension, the radius in our geometry, simply because it does not belong to the universe.
In this hypothesis no coordinate transformation is needed, all our physics can be applied to the whole universe. But the whole universe moves, changing over time.
It would seem, then, we cannot apply laws such as entropy to different stages of growth.
The expansion model, however, has its geometry. This will allow to convert laws and apply them to those different stages.