The void theory

On tumblr, one of my reader, frankietwohats, ask me the following question:

Can I ask you a random question? I can't remember the name of a theory that argued that the universe wasn't expanding, but instead was stretching. Do you happen to know of it/it's name? It came up in conversation today (well, universe expansion did) and I want to look into it more.

I don't know if this is the theory that you intend, but after a briefly research on Google, i find th Void theory. About it, Esther Inglis-Arkell writes on io9:

There was a time that the earth was considered the center of the universe. Then it got knocked out of the way by the sun, and ever since then the astronomer's mantra was, "We are nothing special." The part of the universe the earth resides in can't be any different than any other part. It's not unique, or remarkable, or even out of the ordinary. Void Theory contradicts all that. Instead of sitting in a typical part of the universe, the earth sits in an unusually empty part; a void. The universe isn't expanding due to some mysterious force. It's just that when light comes from a denser part of the universe and trips across the void, it is altered to make it look like the universe is expanding. Since this exansion is the same when observed from any part of the earth, the earth has to be roughly at the center of this void. Suddenly, the observable universe is geocentric again.

But... what is the void theory?

This diagram reveals changes in the rate of expansion since the universe's birth 15 billion years ago. The more shalow the curve, the faster the rate of expansion. The curve changes noticeably about 7.5 billion years ago, when objects in the universe began flying apart as a faster rate. Astronomers theorize that the faster expansion rate is due to a mysterious, dark force that is pulling galaxies apart.

First of all, following Clifton, Ferreira and Land⁽¹⁾, we must remember that our picture of the universe is based on the following two principles: the spacetime is dynamical, obeying to the Einstein's equations; the Universe is homogeneous and isotropic on large scales, that is a generalisation of the Copernican Principle that the Earth is not in a central, specially favored position.
Now, the exact solution of Einstein's equations was provided by Lemaitre-Tolman-Bondi spacetime \[\text{d} s^2 = -\text{d} t^2 + \frac{Y'^2}{1-K} \text{d} r^2 + Y^2 \text{d} \Omega\] In this model there are four free parameters: the density at the origin, the density and radius at the midpoint, and the radius at which we match to Einstein-de Sitter spacetime⁽²⁾. Instead the void model:

is completely specfied by the radial profile, the Hubble rate at the void centre today, $H_0$, the radiation density today, which is fixed by the CMB mean temperature, $T_0 = 2.725 K$, and the baryon fraction $f_b = \frac{\rho_b}{\rho_m}$. Outside the void we asymptote to EdS.

The curvature for three different types of voids

From the bibliography of the first two references, we can extract some interesting papers about the void model. On of the oldest seems be Celerier's work about an inhomogeneous model constructed from Lemaitre-Tolman-Bondi spacetime with a cosmological constant equals to zero⁽³⁾. A not so different model (it start also from the Lemaitre-Tolman-Bondi spacetime) was developed by Alnes, Amarzguioui, Gron⁽⁴⁾. In the model

there is a continuous transition between the inner underdensity and the outer regions. Therefore we consider an isotropic but inhomogeneous dust dominated universe model, where the inhomogeneity is spherically symmetric.⁽⁴⁾

And, if our universe is homogeneous, we can infer the time evolution of the cosmic expansion simply from the observations, because the expansion rate depends only by time.

Therefore, if the expansion rates inferred from observations of supernovae are larger for low redshifts than higher redshifts, this must be attributed to cosmic acceleration in a homogeneous universe, whereas in our case it can simply be the consequence of a spatial variation, with the expansion rate being larger closer to us.⁽⁴⁾

Alexander, Biswas, Notari and Vaid developed instead a minimal void model

with minimal length scale and underdensity contrast that is required to give a consistent fit to the supernovae data.⁽⁵⁾

The results of the group seem positive:

We find that the Minimal Void (MV) model can consistently account for the combination of the Type Ia supernovae, WMAP 3rd year, BBN constraints (...) The MV model can accommodate reasonably all of the data considered, although the fits are not as good as the concordance model.⁽⁵⁾

But there is a little problem:

On the other hand we have seen that the Minimal Void is in trouble with the Baryon Acoustic Oscillations measurements⁽⁵⁾

And this is one of the most important problem found by Zibin, Moss, and Scott in all void models: indeed the BAO poses strong constraints to this alternatove model to dark energy⁽²⁾.
The conclusions of the work⁽²⁾ are not so optimistic about the future of the void models, and Zibin says to the EurekaAlert's press release (via Universe Today):

Void models are terrible at explaining the new data, but the standard dark energy model works very well.

It sounds similar the following comment on the New Scientist Space Blog:

Clifton's results are very speculative⁽¹⁾ - there's no hard evidence that suggests we live in a void, nor is the existence of a void that huge very feasible according to the standard model of cosmology. And even if the void theory could account for the supernovae observations, it wouldn't explain supporting evidence for dark energy from the cosmic microwave background, relic radiation from the big bang. Better observations of more supernovae - from, for instance, the proposed SNAP experiment - could help test the theory by gauging how the expansion rate of the universe has changed throughout cosmic history.

But I would conclude with Clifton's words:

Two very different paradigms have been invoked to explain the current observation of an apparently accelerating Universe, depending on whether we invoke or reject the Copernican Principle. We have shown that in the coming years it will be possible to experimentally distinguish between these two scenarios, allowing us to experimentally test the Copernican Principle, as well as determine the extent to which Dark Energy must be considered a neccessary ingredient in the Universe.⁽¹⁾

So only future observations could confirm the dark matter-dark energy universe, or the void universe or another scenario.

One of the most complicated and dramatic collisions between galaxy clusters ever seen is captured in this new composite image of Abell 2744. The blue shows a map of the total mass concentration (mostly dark matter).

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(1) Clifton, T., Ferreira, P., & Land, K. (2008). Living in a Void: Testing the Copernican Principle with Distant Supernovae Physical Review Letters, 101 (13) DOI: 10.1103/PhysRevLett.101.131302 (arXiv)
(2) Zibin, J., Moss, A., & Scott, D. (2008). Can We Avoid Dark Energy? Physical Review Letters, 101 (25) DOI: 10.1103/PhysRevLett.101.251303 (arXiv)
(3) Célérier, Marie-Noëlle (2000). Do we really see a cosmological constant in the supernovae data? Astronomy and Astrophysics, v.353, p.63-71 (arXiv | scan | pdf)
(4) Alnes, H., Amarzguioui, M., & Grøn, �. (2006). Inhomogeneous alternative to dark energy? Physical Review D, 73 (8) DOI: 10.1103/PhysRevD.73.083519 (arXiv)
(5) Alexander, S., Biswas, T., Notari, A., & Vaid, D. (2009). Local void vs dark energy: confrontation with WMAP and type Ia supernovae Journal of Cosmology and Astroparticle Physics, 2009 (09), 25-25 DOI: 10.1088/1475-7516/2009/09/025 (arXiv)