
In the standard ΛCDM model of the
cosmos, the broad structures we see today (galaxies clusters) are thought to
have formed from primordial quantum fluctuations in the early (observable)
universe. These fluctuations were random variations in density so that
over-dense locations formed galaxies and under-dense areas formed what is
called 'voids'. The over-dense regions became increasingly over-dense and voids
became increasingly under-dense as the cosmos expanded. On top of the normal cosmic
expansion, matter inside a void would tend to move outward due to the
gravitational pull of the surrounding denser regions.
Even if the cosmos at large was not expanding, an observer near the center
of a void would still have noticed something like Hubble's law, i.e. more
distant galaxies receding faster than nearer ones. Hence, this concept is
called the "Hubble Bubble".1 It has been shown that
under certain conditions (e.g. our region with all its superclusters, is near
the center of a 'super-sized void'), it could even give an apparent accelerated
expansion in the larger universe - hence mimicking dark energy.
The main problems with this idea are: (i) it seemingly
requires our galaxy to be near the center of a void, which is apparently not
the case; (ii) the rate at which galaxies would recede from us would be too the
low for what we observe today, unless the void was unrealistically large (some
billion years across) (iii) We are much more likely to live inside a "void
wall", the dense structures that surround voids. Surprisingly, this
location would give the same type of apparently accelerated expansion.
For the relatively nearby "Hubble
galaxies",2 it would give redshifts according to Hubble's law,
but when we look at the range of the supernovae where the accelerated expansion
was observed, we observe on the far
side of a void. Due to the void characteristics, those galaxies would be
farther away than they should be for a matter-only cosmos - hence apparent
acceleration of expansion. There were still quite a few problems with this idea,
amongst others, it would still require some dark energy to fit observations.
Since late 2007, a New Zealand
cosmologist, David Wiltshire, has been advocating an improvement to this
scheme, apparently solving most (plus a few extra) of the Hubble Bubble
problems. It has not been convincingly refuted up to now. He calls it
the 'Fractal Bubble' (FB) 3.1 or 'Timescape'3.2
cosmic model, which includes a few very interesting, but entirely reasonable
ideas. The main three are: (i) the voids and walls of the cosmos forms a
fractal structure (i.e. scale-independent); (ii) the cosmic time of the voids
and walls are different, because they comply strictly to Einstein's
gravitational energy and time dilation; (iii) the cosmos is about one billion
years older (on average) than what the standard ΛCDM model predicts, which also
solves some additional problems.
The standard ΛCDM model works only on the average density of the cosmos
(i.e. homogeneous matter), giving a surprisingly good fit to observations; but
- many of the interpretations and values derived from the data using the homogeneous
ΛCDM model as departure point. Hence, the results are model dependent. For one
thing, it uses a 'cosmic time' that ticks at the same rate everywhere in the
model. As can be seen in NASA's 'cosmic map of local structure',4
the roughly 500 million light years radius around us is not homogeneous at all.
At larger distances, the voids are apparently even larger (not shown on this
diagram).

Wiltshire has shown that when he uses a
non-homogeneous density model and assumes that the large voids comprise more
than 50% of the volume of the universe, there may be up to a 43% difference
between 'void wall clocks' and 'void center clocks'. This effect is due to
Einstein's standard gravitational time dilation and the combined inhomogeneous
density and time progression [Wiltshire3.2 Fig 1(b), right] cause
effects that appear to be an accelerating cosmic expansion.
If he factors this into his FB model (with voids expanding faster than walls), the predictions are an equal or even better fit to observations than the
standard model. Wiltshire's Table 2 shows a comparison of the ΛCDM and FB
models.

If his sums are right, this table is very impressive. What is even more
interesting, it requires no dark energy! He labels the FB a
'conservative' model, because it requires no new physics. Further, it needs
only half as much dark matter as the ΛCDM model, meaning that normal matter
makes up at least one third of the total energy of the cosmos (against the mere
4% in the standard model). On average, it means we may live in a standard flat
Einstein-de Sitter universe that will not expand forever, but neither will it
ever collapse. A sort of relief…
Personally, I do not understand his model very well (I doubt if very many
cosmologists fully understand it, or have even seriously looked at it), but I
did not see any devastating critiques against it. Some of the critiques seem to
confuse it with 'Hubble Bubble models', where the observer is near the center
of a void. In the FB model, bubbles play a very important role, but they do not
have to be excessively large. The only requirement is that they make up more
half of the cosmos by volume, which is apparently the case (counting in the
mini-voids, the FB model requires a void-to-wall volume ratio of about 70:30
presently).
Jorrie
Notes
1. The pretty bubble picture top left is from David Wiltshire's home page: http://www2.phys.canterbury.ac.nz/~dlw24/. 'Fractal Bubbles" are not quite the same as "Hubble Bubbles". I combined them in the title for effect... :)
2. 'Hubble galaxies' refer to those on which Edwin Hubble originally based
his linear redshift-distance law. They were all well within 100 million light
years from us. He was a bit out on the value of the constant Ho, but
that was due to distance measurement errors, which were corrected much later.
3. David L. Wiltshire, (3.1) Dark energy without dark energy, Dec, 2007 and (3.2) Gravitational energy as
dark energy: Cosmic structure and apparent acceleration, Feb, 2011.
4. A better resolution diagram can be viewed at
http://heasarc.nasa.gov/docs/cosmic/gifs/atlas_sc.jpg.
5. I want to acknowledge the stimuli given by jonmtkisco and Cedar in my Blog Alternative cosmologies. Jon originally drew my attention to it, but I thought it an improbable theory at that time. Cedar's ideas made me look at it again and I now no longer think it is that unlikely... 
-J
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