AWT is fully consistent with ekpyrotic cosmology, while branes are generally considered a density gradients of Aether. Which basically means, observable Universe passes through density gradient of Aether, which results in omnidirectional space-time expansion. Because of fractal foam nature of branes and time dimension, it's probable, this expansion would change it's direction in less or more distant perspective, but it will never repeat in the same way. It means, AWT is somewhere between aperiodic (i.e. Friedman's cosmology, for example) and cyclic cosmology.
Brane cosmology is directly testable both in space, both in time dimension, because it manifests both in foamy structure of dark matter, both in gradient of space-time expansion, i.e. by the Doppler anisotropy of cosmic microwave background radiation (CMB). From time perspective we should observe a change of gravity constant with time, because observable portion of Universe passes through more and more dense Aether gradually (we can interpret it like fall into giant black hole). This behavior leads to new interpretation of classical theory of expanding Earth, but it can be tested in even more straightforward ways.
Because observable matter has a greater density, then the vacuum, we can consider it as a pieces of pre-collapsed Aether foam. During space-time deforms, these peaces would behave like more stiff and the density difference between Aether foam forming matter and vacuum will cease to zero. Because the gravity force and gravity constant depends on this density difference, it will decrease too with time. We can even observe it in real time for example by gradual decrease of mass of kilogram prototype - as it virtually dissolves in collapsing vacuum (compare the proton decay, as predicted by Standard model).
We should realize, we cannot detect the change in light speed in expanding space-time, until we use measure based on standing waves of light (i.e. laser resonator in contemporary SI system of units) for meter definition. But when we use a solid rod as a reference measure, we could detect change of light speed related to this measure - after then the gravity constant would remain constant, just the light speed will change - so we shouldn't detect any change in fine structure constant anyway. By some theorists change in speed of light is interpreted as a disappearance of time from our Universe, but such interpretation is apparently dual to variable light speed concept and/or accelerated space-rip, as interpreted by other cosmologists.
The more dense vacuum is, the less stable are all material objects in it, the smaller amount matter is sufficient for phase transition of stellar mass. Therefore the decrease of gravity constant is followed by gradual decrease of luminosity of periodic flashes of type Ia supernovae cefeids (so called the standard candles), which would appear more remote and frequent, then those in constant gravity field. From this perspective the speed of Universe expansion would remain constant (i.e. no dark energy should be required) - just the gravity constant or speed of light will change. These insights render our Universe a much more dynamic, then we ever expected before - but we should realize, they're plural and as such they shouldn't be mixed mutually.
The annual motion of Earth in Aether density gradients should manifest by subtle annual changes of gravity constant or light speed, too. This possibility was opened recently and it can be tested easily by correlation of annual changes in gravity constant to spatial orientation toward Virgo cluster and Rubin-Ford anisotropy.
More dense vacuum in direction to Virgo cluster should increase the speed of heavy element decay, because it weakens all attractive forces, not just the gravity. This annual change in decay rate of heavy elements was observed recently at the case of Si-32 and Ra-226 elements, which was correlated to Earth-Sun distance and possibly the catalysis of decay by solar neutrino flux. Again, the correlation of these observations with CMB anisotropy can help us decide, which explanation is more relevant here. As we can see, even quite rough logical approach brings a number of testable predictions and connections here.