The universe has no shape. we are observing in directions and see as far as we see the first notable obstacle. In most directions we see nothing, is there a void or an empty space? A void is without existing objects but there are many “dark” things there — short strings of momentary potentials called pre-things and pre-interactions — so void is not empty, it is only void of existing things.
Looking at the universe from outside it, it would be a very unsymmetrical nonconvex thing with curved peaks and whirling tunnels. If it would be a perfect sphere for example maybe the light if non-acted upon will travel on circular geodetics, so eventually you may see your own back one can say. But with the space light is curved by all interactions ( in fact it could be that one photon in the universe is trying to follow a circular orbit depending on the diameter of the universe so to speak, not a straight line), in particular by gravity effects.
So the orbit of light in the universe is a rather twisted curve far from a straight line. yet we calculate distances by the red shift of the emitted light, as if it is moving away from us in a straight line, thus also acting as if we are the centre of the universe. Well it is only an approximation. Yes, but how good is it?
If we would have special glasses while looking from outside of the universe to it so that we could see the non-existing part of reality, the universe would even be more amorphic. Places are dynamical in the existing universe, for non-observed things we cannot establish a place for it (and even if we can it is the wrong place because we “see” the places where it evolved long ago in the past). Humans cannot escape the mathematical dogma in their head, the belief that the universe is a very regular creation goes back, even unaware, to the creation myth of God creating some, perfectly shaped things strictly organized by what we see as elegant laws. Well it is more chaotic then we can imagine and that is perhaps its real beauty.
The universe is in continuing creation. The Big Bang was the exodus into existing reality from the existence void, once things existed we can speak of dynamic places of things existing at some non-trivial existence time interval (not a moment!). The place we think we see when observing an existing object is not the place of one existing manifestation but a sequence of places of existing manifestations of the existing object over the longer observation time period containing many existence intervals. So even for the photon , what we observe are many manifestation of the e-photon in the time period of observing the o-photon (what we call the photon!). Anyway, when the exodus into existence began we may associate places to the first existing things and the process started in very many , probably even disconnected places. that process of things popping up in existence (and also some disappearing into nothing) is always going on. The start of the process of existing is in some (creative) pre-thing in a state at some moment in time and that creative pre-thing does not have a history in time for the transition correspondences linking the states which are totally ordered in time. Thus the universe is growing and also shrinking, in the beginning only growing but there may be some culmination point where it will be shrinking. The density of the universe in terms of existing things can be defined and it is varying over time. By some plausible continuity assumption (as an axiom without proof though) one may think that the change from densifying to thinning does not happen momentarily — this is very plausible because existing is at non-trivial time intervals — so there are longer periods of growing followed by shrinking periods. Nothing grows forever but it could it shrink to nothing? Well it could shrink back to a void and then start again with a new exodus into existence when the activities in the darkness of the void lead to enough “cohesion” of pre-things for them to start to exist. It is possible that the end-void remains void forever…the non-existing universe of too short strings, and even it could finally become empty, nothing comes out of emptiness, … end of the universe!
In conclusion here, the shape of the variable universe is not defined. If you assume light is moving on geodetics for the configuration universe then it is clear that the manifold model of relativity is much to simple to describe the more chaotic structure we described, not to mention that the assumption everything is measurable by real numbers is completely without evidence, again that is just the mathematical dogma in people’s minds.
Expanding universe? The growing of the universe should be first expressed in some density, we cannot observe the changes in density in the universe as these processes are everywhere — but that means far away! — and very very slow, meaning over millions of years, that is fast on the scale of the universe, but for human observations (forever?) out of reach. The growing and shrinking — going on simultaneously — influence the shape one may define on existing reality by some ad hoc geometric constructions in our abstract world. Whereas cohesion is an interesting field (as in quantum fields) in the non-existing reality it can also play a role in the macro-world, it may in fact explain the existence of gravity as an effect of the cohesion field in the universe. Cohesion would be a counter-action to expansion if the latter would be a true phenomenon, it could also lead to a force behind the shrinking. the varying shape of the existing universe then would appear as a balancing between growth and shrinking, peaks would get smaller while pits are getting less deep. Depending on energy movements in the universe those actions would alternate and shift around making the universe into some bubbling soup like a pudding cooking on the fire. There are places defined abstractly — even in states at moments and for short (shorter than existence intervals)strings of pre-things — but only existing things can occupy some real dynamic place. So with the growing and shrinking in density over very long periods for us observers, plus the structure of the non-existing part of reality, we cannot make a good notion of the chaotic shape of the dynamic universe on the basis of correct directions and approximate measurement of the distance of first objects blocking our view (and we do not see what is straight behind that unless it would be immensely bigger; in what case we would probably not distinguish the smaller light source within the bigger, even with some light variation in luminosity). It is possible the universe is expanding but locally and not at constant speed but also in certain time periods, it may be shrinking again locally over some time periods afterwards. To understand these global waves of change one has to know all the ongoing changes in the universe both micro and macro. so i would ,for now, conclude that the changes in the unknown global shape are too chaotic to fit in the notion expand or contract.
In the beginning we thought earth was flat, then earth was the centre of the universe a perfect square with lights on the surface to light up our nights, the all planets were circling around the sun and afterwards the orbits became deformed somewhat as variations on the theme of elliptic shapes. It seems that in each step we started from the same false premisses, centres, spheres, regular shapes and movements, from straight lines in Euclidean space to curved geodetics on some manifold in relativity and more chaotic quantum trajectories.
The more chaotic structure depending on cohesion and density created by continuing creation starting in moments by creative pre-interactions is the beautiful organic structure of a dynamic shape taking into account all effects in reality!
God did not use our mathematics, I guess It has a structure of its own!