Hypatia
Hypatia is the name given to the 5D spherical body around which the brane of our universe is wrapped. The 4D brane manifests locally as hyperbolically curved space, modelled by the interior of a sphere which tightly contains a torus (donut) with a zerosized central hole; the torus is excised from the sphere's interior and the observer is placed at the origin (center) of the sphere. The remaining volume within the sphere represents our hyperbolically curved space, by which if we travel a characteristic distance R, the area of the shell of space reachable is not the 4πR² of flat Euclidean space, but rather 4πR²/(1R²/T²)² (approx) , where T is the maximum possible distance. Thus our universe is finite but unbounded, and negatively curved.
Why such a model? 100 years ago Einstein took an apparently absurd observation, the invariant speed of light, and turned it into a theorem which revolutionised our knowledge of physical law. Today, too, we have observations, notionally absurd, but which point the way to further understanding. These observations are:
The Hypatia model of the universe elegantly accomodates all these observations.
A 5D sphere, rounder than we know, Hypatia is an ecosystem of which its undulating surface, our universe, is a bit player. 
Divergent geometry of the hyperbolic space goes as the surface of a torus of zero aperture, from its center. Einstein modelled such a curvature as part of his static universe, but extended it outwards a brief way without closing the curve by wrapping it around the torus, as do the radial lines (emanating from the centre) in this illustration (right).


Motion thru the manifold is modelled by the observer remaining at the center and the torus flexibly rotating thru its centre; thus the spatial curvature remains unchanged regardless of the observer's travels. In this illustration (left), leftward travel involves the upper limb of the torus turning counterclockwise and the lower limb turning clockwise, in tandem.

How does the Hypatia model reconcile the observations presented on this page?

This page does not try to explain too much. A key point is that the rate of time flow (originating, like gravity, from Hypatia) increases with the passage of time. It is a derivative function only, and serves to distinguish past and present. This is interpreted in the bigbang cosmology as physical expansion. But time is a more sensible candidate for change than physical size, as was known for the first 20 years after the redshift was discovered. The 5D curvature means that photons crossing between dissimilar places (i.e. different 5D hyperangle) will impact with a vector component pointing back to Hypatia  thus a fraction of them disappear from our universe. This accounts for the "missing Solar neutrinos" problem. Another key point is that matter recycles out and in of our universe; black holes represent the exiting of highentropy matter out of our universal brane back to Hypatia, and young galaxy centers and quasars represent the reintroduction of lowentropy matter back into our universe from Hypatia  they are gravitational towers from which matter falls into our universe, and double radio lobes also appear to be matter "falling" out of galaxies' poles via 5D gravitational slopes. Black holes do the same but are gravitational funnels exiting to 5D Hypatia and so are very dim of course.
Want hard math? Look at this paper by Ichiki, Garnavich et al which describes the salient points. For an early nonmathematical description see this January 1998 posting done by your correspondent, after I saw all this during a XmasNew Year holiday at a New Zealand South Island holiday house overlooking the Pacific. Through the sound of crashing waves I saw only the dimensions, the gravity, the quasars, the geometry and the math  but pardon the prose (both here and in this posting titled "Odyssey to Hypatia" ).