In AWT theory the definition of space depends on definition of space-time, so that the definition of space cannot be separated from definition of time due the mutual symmetry of transversal and longitudinal wave spreading through Aether. This relation is one of most important finding of relativity theory, albeit rather unconscious / ad-hoced at Einstein's times - so that Aether theory extends the understanding of this relation to duality of space and time.
In AWT analogy the space-time is the density gradient, forming water surface. The space dimensions are the directions (space-time dimensions) planparallel to water surface, while the remaining direction (a time dimension) is normal ("perpendicular") to water surface. This model explains naturally the symmetry of space dimension and the asymmetry of time dimension (so called the time arrow), the various number of space and time dimensions and much more.
Surprisingly, nobody has pointed to this trivial analogy in physics after one hundred years or relativity theory development - isn't it somewhat strange? Anyway - it's apparent, both time, both space has a robust meaning in physics. If we admit, here's no space, we should admit, here's no time as well - and how we could explain the tangible difference in time and space symmetry (space has no arrow, so we can move along it rather freely), the various number of spatial and time dimensions of space-time and so on..? If something makes a difference, it must exists, because difference is, what makes things real in AWT.
The causal space-time is the place, where density of Aether exhibits some density gradient, so it can behave like water surface, which can serve for transversal wave spreading, i.e. for causal energy propagating at distance. Therefore the scope of space always correspond the scope of causal time arrow, which is virtually unlimited because of infinite mass/energy density of Aether by definition. Infinite (or zero) things usually doesn't need any further explanation from human perspective. Every fixed number is suspect from strictly causal perspective and as such it needs an even deeper explanation. Until the time is infinite by definition, the space remains infinite, too.
Space is always "empty" by definition, because motion in it doesn't requires, neither excerts an energy. If space could be visible, it would become a observer object in space. No pin-point object can serve both like subject of observation, both like mean of observation at the same moment, from this the deep misunderstanding of Aether concept follows. Aether cannot be observed, until it serves as a luminiferous medium of space-time by definition - therefore the speed of energy spreading is always invariant by definition and it has no reference frame in space. If we are moving under exchange of energy with environment via dispersion or during climbing to hill, we can be sure, we are moving in space-time - not just space. If we could observe space, it would mean, space isn't space anymore. Due the nonlocality of every observer and observation process in space-time (real observer isn't never pinpoint object by the same way, like every observation at distance takes some nonzero time), the emptiness of space is always violated by the same way, like the Lorentz invariance at all space-time scales.
Because scope of space is delimited by scope of transversal energy spreading from local perspective of any observer, the limitation of space (and time) scope is the speed of causal energy spreading from observer, the light speed in particular. Therefore we can say, radius of observable Universe corresponds the speed of light spreading multiplied by age of observable Universe.
Another limitation of space concept is the scope of causal energy spreading along single time dimension. Whenever observer starts to move in another time dimension(s), we are saying, it undergoes a dispersion or compactification. Due the presence of cohesion forces inside of object, dispersion usually begins at surface - so we are saying, it collapses or evaporates. The evaporation of water or meteors during their fall through Earth atmosphere, the evaporation of matter in contact of magnetosphere of magnetars or during fall into black holes are all dispersions of energy wave packet forming observable object from AWT perspective. Therefore inside of observable Universe the space is limited by stability of observer - it cannot cross the boundaries of observable space, or (s)he would follow another dimensions of space, i.e. (s)he would collapse and/or evaporate into smaller particles of matter, or even into pure energy, i.e into radiation.
From symmetry of time arrow follows, every dispersion of matter into smaller particles bellow observer scale is followed by some compactification of smaller particles into large objects above the observer scale. We aren't considering the dispersion or collapse as a traveling in time usually, but this is exactly, what these things means in AWT. Note that the dispersion corresponds the traveling into past, whereas the collapse denotes the traveling into future with respect to omni-directional space-time expansion. The observer space-time scale usually defines the local boundary between both time arrows. Due the breaking of symmetry between insintric and exsintric perspectives (every local object appears like part of global object, inside of which it resides), the symmetry of space-time arrows is violated toward a dispersion from local observer perspective, so we tend to believe, entropy of Universe increases as a whole.
Of course the boundary between time arrows isn't always completely sharp due the particle nature of space-time gradient by the same way, like symmetry between insintric and exsintric perspective (i.e. the boundary between space and observable objects inside it). When symmetry of dispersion is broken, we are talking about refraction, the gravitational lensing in particular. For example dark matter can serve both like space, both like observed object. With compare to various field theories, AWT doesn't require some tangible particles for dark matter to exist. In AWT interpretation the streaks of dark matter can be simply formed by more dense areas of Aether foam. Such dense areas exhibits a refraction, when observed from distance - but from proximity they appear like normal transparent space-time.
The dispersion means, the transversal character of energy spreading and uniqueness of time arrow is violated, at least for some most lightweight particles, like the photons. Because causual energy spreading is mediated by transversal waves, the dispersion is usually followed by birefringence, which means, some portion of photons from some space-time events spreads in different directions in space depending on polarization of wave - which is impossible from strictly causal perspective. The collapse of object into black hole singularity can be understood as a violation of causality as well. Therefore the presence of some observable objects in space is always connected to some violation of causality and increase of number of time arrows - despite of we usually don't realize it. And every evaporation is manifestation of hidden dimensions of space by the same way, like every dispersion of light energy is a direct manifestation of Lorentz symmetry violation. In this way, AWT unifies our fundamental understanding of space and time and various other concepts by concept of particle environment symmetry.