Simply put, Penrose/Gurzadyan examined the cosmic microwave background data from WMAP and showed that there are these concentric rings of uniform temperature in the CMB. This is not in dispute. What is in dispute is that they concluded that that these are signatures of "... black holes colliding in a previous cosmic 'aeon' that existed before our Universe....", thus, giving an evidence towards a cyclic universe.
That led to a flurry of activities, and 3 groups have independently challenged that view[2,3,4].
To gauge this significance, Gurzadyan compared the observed circles with a simulation of the cosmic microwave background in which temperature fluctuations were completely scale invariant, meaning that their abundance was independent of their size. In doing so, he found that there ought not to be any patterns. But the groups who are critical of his work say that this is not what the cosmic microwave background is like.
They point out that the WMAP data clearly show that there are far more hot and cold spots at smaller angular scales, and that it is therefore wrong to assume that the microwave sky is isotropic. All three groups searched for circular variance patterns in simulations of the cosmic microwave background that assume the basic properties of the inflationary Universe, and all found circles that are very similar to the ones in the WMAP data.
Moss and his colleagues even carried out a slight variation of the exercise and found that both the observational data and the inflationary simulations also contain concentric regions of low variance in the shape of equilateral triangles. "The result obtained by Gurzadyan and Penrose does not in any way provide evidence for Penrose's cyclical model of the Universe over standard inflation," says Zibin.
Of course, that's not the end of it. Gurzadyan/Penrose has posted a rebuttal (also on arXiv). I'm sure there will be more forthcoming to rebut that one as well. People don't even wait anymore for such a thing to be published.
This, btw, is what happens when we try to deduce something using only a set of data and not in possession of other types of data. Often, in such a case, the conclusion isn't unique. You say the data is consistent with A, someone else can also say it is consistent with B. That is why we seldom accept anything to be valid until this non-uniqueness has been sufficiently removed, and Mother Nature clearly points to a single, clear description of such-and-such phenomenon. It is why science can take a very long time to come up with a valid theory of something.
1. Gurzadyan, V. G. and Penrose, R. Preprint at http://arxiv.org/abs/1011.3706 (2010).
2. Wehus, I. K. and Eriksen, H. K. Preprint at http://arxiv.org/abs/1012.1268 (2010).
3. Moss, A., Scott, D. and Zibin, J. P. Preprint at http://arxiv.org/abs/1012.1305 (2010).
4. Hajian, A. Preprint at http://arxiv.org/abs/1012.1656 (2010).
5. Gurzadyan, V. and Penrose, R Preprint at http://arxiv.org/abs/1012.1486 (2010).