Dutchman Willem de Sitter developed an expanding cosmological solution^{[1]} to Einstein's field equations (EFEs) in the same year that Einstein made his "biggest blunder"  1917.
The "blunder" was adding a cosmological constant (Λ) to the
EFE's in order to keep his cosmos from collapsing or expanding. On the
other hand, de Sitter's expanding model sported only Λ and nothing else 
no matter, no radiation, or at least the latter two had no effect on
the expansion dynamics. What's more, de Sitter's model was a rigorous
solution to the EFEs.
Although Einstein could not find any mathematical error in de
Sitter's work, he argued that it could not possibly have any physical
meaning and must hence be just an artifact of the math. After all, the
real cosmos had both matter and radiation energy and it was static, as
far as observations went at the time. Further, his general theory was
all about matter curving spacetime and how curved spacetime affects the
movements of radiation and matter.
When Hubble discovered that the universe was indeed expanding,
Einstein dropped Λ from the EFEs, but the fact that his own theory did
allow a solution with zero matter remained a puzzle. This was 'resolved'
by the fact that Friedman and Lemaitre had already found other workable
expanding solutions to the EFEs, which did not only allow radiation and
matter to enter the model, but they did not need Λ at all.
The
de Sitter cosmic model was all but forgotten, until in the 1980s, when
cosmologists attempted to solve the 'flatness' and the 'horizon'
problems of the standard model that cropped up out of observations.^{[2]} Alan Guth's inflation theory
solved both problems and it was found that it is compatible with de
Sitter cosmology, with Λ of course. When accelerating expansion was
discovered in the late 1990s, it was soon realized that as time goes on,
the cosmos may be heading more and more towards a de Sitter type
expansion. The de Sitter model was then taken very seriously, because it
seemed to describe the 'opening' and the 'end games' pretty adequately.
(Picture on right from http://www.science20.com/hammock_physicist/geometry_big_bang90461. See final paragraph below.)
But what about the 'middle game', which is all we can really observe?
We surely see a lot of radiation, especially in the early midgame and
we observe a lot of matter. Well, maybe not all that much, because today
the radiation energy density is negligible and the normal matter
density is about 4% of what is needed for the 'flatness' we observe. The
rest is dark matter and dark energy  unobserved, with only
"circumstantial evidence".
Since our observational accuracy on things like largescale distances
(and hence the Hubble constant) does not really make the ±4% mark, it
makes one uncomfortable, to say the least. Granted, there are many
corroborating pieces of evidence that point towards the 'bestbuy'
values used by cosmologists today. But, they are invariably all
interpreted along the lines of the currently preferred Lambda Cold Dark
Matter (ΛCDM) model. What if they would be interpreted using the de
Sitter model?
To do such an interpretation is beyond my knowledge, but fortunately there are more capable people around, e.g. the Blog
from where I ripped the picture above. Johannes Koelman did an
excellent job of explaining the science at the heart of the present
thinking in an accessible way. I suggest you give it a read and if you
feel intimidated by the heavyweights on that Blog, you are welcome to
comment here.
J
[1] http://en.wikipedia.org/wiki/De_Sitter_universe
[2] The 'flatness problem' centers on the question: why is space
(not spacetime) of the cosmos appearing to be so near flat on the large
scale? The 'horizon problem' is about answering the difficult question:
why do we observe the CMB to have virtually the same temperature
everywhere we look?

Re: De Sitter Cosmic Model Revival