Personally I don't think the universe randomly grows on its own, at least
not at a very fast rate. While life on the already existing worlds may
expand and/or change, I don't see the universe expanding without some sort
of push. Perhaps every thousand years or so a star explodes, forming a new
world, but the universe as a whole would be too stable for that to happen
more often than once a millennium or so.
As for other possibilities for universe growth, I agree with Alex that
Sovereigns, among other species, may have the ability to make new worlds (or
drastically change the ones that exist by wiping the slate clean and
beginning again), I don't know if they really have a reason or drive to do
so given how many problems plague the world already.