Is the Universe (as whole) cold flat Euclidean space or cold Einsteinium circle space ?
In AWT the answer depends on the observation perspective used. We can compare it to the observation of landscape in fog or spreading of light through foam. From outer perspective foam or fog is quite homogeneous, but from inside every source of light suffers dispersion, so that light path never reach infinite distance here. We can imagine, every source of light disperses by density fluctuations of vacuum, which manifests itself like cosmic microwave background.
We can compare it to the situation of wave spreading on the watter surface. From outer perspective, which is mediated by sound waves spreading through underwater, the water surface appears flat. But the surface wave suffers by dispersion on density fluctuations of watter, which are caused by Brownian motion of water molecules
As the result, ripples at the water surface spreads by slower and slower speed, so that the rings speed decays to zero and they're becoming more and more dense gradually. The answer is, from outer perspective Aether is of infinite mass/energy density and as such it's always flat. But from limited perspective of inner observer the light always suffers by dispersion, so it spreads more and more slowly, which we can interpret
like dark matter cloud, surrounding every massive object. And the space-time defined by such light spreading is always curved. The duality of insintric and exsintric observational perspective is quite important in AWT and it affects most aspects of our observation, for example
uncertainty principle.
So that my answer could sound: Universe is flat from perspective of gravitational waves which spread in superluminal speed, but it remains always curved and closed from perspective of light waves, which are spreading in limited speed.