Of cause this is maybe not a fact either. The space has 3 dimensions and the 4. dimension is more connected to the matter how we think the whole space of the universe. If we think there is all and no outside, as everybody normally thinks in astronomy and philosophy, mathematically it is so easy as to put one vector more. Is it really a space dimension or something else, for example a wholeness- dimension, not e space- dimension, is dubious. Anyway we can take it as a dimension as well as we take the time as a dimension in the equations. So we can also speak of the 3+1+1 dimensional universe. Three space- dimensions, one- time dimension and one wholeness- dimension. All taken as vectors in mathematics, even if that is a simplification of the reality. But the important thing is that all these five things really exist in the physical reality. Other dimensions are dubious. The spirit world is only a thing of the religions and the human life, and maybe particle physics (if there exists spirits), but not a question of the cosmology.
But we can not be dogmatic in the cosmology. Whenever we find something new, it has its consequences for the whole packet. When we found that the earth is revolving we abandoned the sun as the center. When we found the going away of the galaxies, we thought that the space is expanding and not static. When we think the space has 4. dimension, it has some meaning to the whole packet.
1) The space
2) The time
3) Other possible "dimensions", (if found, not before), and the things in QT
4) Matter (quantums, atoms, stars and galaxies as the most important things) and energy
5) Forces (gravity as the most important thing) and radiations (light and else)
6) Movements and developments
Which are the changes we must do to each level if we take the 4. dimension seriously? Is it a fact that this has not really studied?
The time for example will not be the same. There is no time for (the space of) the universe, because it is not a moving particle. And already now the time is different as the 3 space- dimensions, it goes only to one direction, it changes with the speed, it exists only in the present (the time is the most difficult thing to understand). The galaxies will move in a 4. dimensional space and not in a 3. dimensional space. Is it possible that this explains the red shift without expansion? To movements the 4. dimension means that the space can not expand. For the universe it means that there cannot be "other universes", because there is no space for them.
Whenever something changes in our understanding of the parts of this wholeness, it has some meaning for the other parts and the view of the whole cosmology. Nothing is eternally fixed in the cosmology. The same as in all the science until we know everything.