One major difference between a hypothesis and a theory is the amount of conjecture.
A hypothesis is a sketch. A theory is a complete model.
Today's standard narrative would have us believe that the Universe is about 13 billion years old, give or take. The number has recently been altered slightly for everyone's convenience (by subtracting a couple of billion years, I believe, to fit some newly discovered "facts" concerning the background radiation).
According to the same narrative, the age of the Universe is the amount of time that has elapsed since the Big Bang.
And, there's the rub.
The rate of expansion (recently found to be accelerating) is said to have been, in some instances, superluminal (i.e. faster than light).
Even though the Universe consists of mostly "empty" space, or "spacetime," if you will, there are still trillions upon trillions of stars in it: that's a lot of mass traveling at neck-breaking speeds all over the place, forming tons upon tons of inertial frames of reference and, therefore, tons upon tons of occurrences of the Twin Paradox overlapping one another. A split-second here is a few billion years over there, and vice versa (whether overlapping instances of the Paradox cancel each other out or, conversely, become intensified, is anybody's guess). What happens when something is moving at superluminal velocity relative to its neighbors? Does its local time begin to move backwards?
The idea of "the age of the Universe", when you think about it, sounds suspiciously Newtonian: a relic from a period in the history of astrophysics when pondering on such matters was far more local. And, I hasten to add, classical, i.e. Einsteinian, relativity, though seemingly more advanced, still assumes that the laws of physics are exactly the same everywhere: a hypothesis we have no hope of ever turning into a theory because experiments yielding any kind of evidence, favorable or otherwise, are not even possible.
Equally impossible, it seems to me, is the task of taking into account all the variables when we estimate the Age of the Universe. Is 13 billion years really a sufficiently well-calculated guess to merit the title of theory rather than just a hypothesis? Is the age of some stars a great deal less - or a lot greater - than we assume?
Is the age of the fabric of space (or spacetime) exactly the same everywhere?