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The current "standard model" or concordance model of cosmology is Lambda CDM which includes late time acceleration due to a cosmological constant, cold dark matter as the missing matter component and an inflationary period at very early times.

What alternative theories are also consistent with current observational data?

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What alternative theories are also consistent with current observational data?

There is an alternative line of thought according to which inhomogeneities in large-scale structure, known as voids, are responsible for the "perceived" or "apparent" acceleration on large time scales. This viewpoint was first advocated by Celerier and Inoue and Silk, among others.

A numerical comparison of WMAP3 data with LCDM and non-Lambda model is done here. It is found that the likelihood of the non-Lambda model is comparable to that of the LCDM one. However such a fit requires a very low Hubble rate ( $ \sim 0.40 - 0.45 h^{-1} $ ) compared to the widely accepted $ \sim 0.73 h^{-1} $, and also requires a significant amount of negative curvature.

These shortcomings aside, a very recent work by Hael Collins allows an analytic approach to the problem, albeit in a simplified setting. To quote from the abstract:

This example provides an illustration of a universe where the inhomogeneities can affect its average expansion rate; and its simplicity allows a condition to be derived that tells when their presence should begin to become important. Since the averages of the non-uniform parts of the metric and the matter density grow faster than their uniform parts, the average expansion rate accelerates with the advent of the era governed by the inhomogeneities. (emphasis mine).

So as they say, you free to "worship at the church of your choice" :-D

[Update: Nov. 14, 2010]

... but if these (1, 2) references to papers by David Wiltshire have anything to say about the question of "apparent" vs. "actual" cosmic acceleration, it would appear that many in the cosmology community have been worshipping the false god of "dark energy" !

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Penrose's Conformal Cyclic Cosmology‎ is such an example. There is late time acceleration due to Lambda, but no inflationary period in the beginning. The late universe is equated to the beginning (of the next big bang cycle) through a conformal factor which maintains the physics.

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To what extent has this been compared to observational data? – j.c. Nov 3 '10 at 15:04
It does make some predictions regarding the distribution of irregularities in the CMB. Basically black holes in the previous aeon should show up as circular patches of colder or hotter radiation. Some such irregularities have been found but more investigation is needed. – Sklivvz Nov 3 '10 at 17:28

Prof. Alex Mayer has proposed a new cosmology that matches observables and which does not require dark energy. Google "Alex Mayer" (his website is the first hit) and then first review the "An Introduction to the New Cosmology" talk he gave in September. You can also download a preview of his new book.

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