I read the paper. It's actually a cool idea. Basically they studied in detail the dynamics of what happens when very heavy stars collapse to form black holes in a universe with four dimensions*.
In three-dimensions, when a star collapses, the outer layers get blown out into space and the inner layers collapse to form a black hole. The black hole being surrounded by the two-dimensional surface know as the event horizon. The surface past which light cannot escape.
However the authors have found that this isn't what happens in four-dimensions. The inner layers collapse into a black hole and are surrounded by a three-dimensional event horizon. However all of the outer layers don't explode out randomly into space like they do in three dimensions.
Some of the outer layers form a thin-sheet, a three dimensional sheet, that looks like an extra layer on top of the event horizon. This sheet then expands slowly away from the star, as it has enough momentum to escape the collapse.
It turns out that this sheet, when taken as an object on its own, is identical to the Big Bang solution of General Relativity in three-dimensions. So an entity living on this sheet would see data consistent with there being no fourth dimension and everything originating from a point in the distant past.
Usually the singularity in General Relativity is taken to mean some approximation or assumption is breaking down. This model would say that as we rewind time we eventually reach a point before the star collapsed and our universe merges with the other layers of the star and can no longer be considered an independent object.
In essence, this model says our universe is "really" a slowly expanding bubble of stellar material, one of the mid layers of a hyperstar** that went supernova. The gravity of the black hole that that star collapsed into keeps the layer compressed and effectively three-dimensional, but the energy of the supernova blast gives it enough velocity to slowly escape from the black hole and so it expands. Living inside this sheet, we perceive this expansion as the cosmological expansion of a three-dimensional universe.
I think the idea is in too early a stage to comment on. The author wants to do better simulations to see if it matches current cosmological data. The model currently matches some observations, but the three-dimensional universe this model produces is scale invariant. Basically its Cosmic Microwave Background (CMB) has an equal number of photons of each energy. Where as our universe shows slightly more photons at some energies.
However it's possible this model does produce a universe like ours, but the current methods of analyzing it are too weak to demonstrate this, or perhaps depending on the conditions in the hyperstar the three-dimensional universe has different CMBs.
*I'm ignoring time in this post.
**Hyperstar refers to the four-dimensional star.
Edited by Son Goku, : No reason given.