I’ve never really thought of this blog as a vehicle for promoting my own research in cosmology, but it’s been a while since I posted anything very scientific so I thought I’d put up a brief advertisement for a paper that appeared on the arXiv this week by myself and Ian Harrison (who is a PhD student of mine). Here is the abstract, which I think is pretty informative about the contents of the paper; would that were always the case!
Motivated by recent suggestions that a number of observed galaxy clusters have masses which are too high for their given redshift to occur naturally in a standard model cosmology, we use Extreme Value Statistics to construct confidence regions in the mass-redshift plane for the most extreme objects expected in the universe. We show how such a diagram not only provides a way of potentially ruling out the concordance cosmology, but also allows us to differentiate between alternative models of enhanced structure formation. We compare our theoretical prediction with observations, placing currently observed high and low redshift clusters on a mass-redshift diagram and find – provided we consider the full sky to avoid a posteriori selection effects – that none are in significant tension with concordance cosmology.
The background to this paper is that, according to standard cosmological theory, galaxies and other large-scale structures such as galaxy clusters form hierarchically. That is to say that they are built from the bottom-up from a population of smaller objects that progressively merge into larger and larger structures as the Universe evolves. At any given time there is a broad distribution of masses, but the average mass increases as time goes on. Looking out into the distant Universe we should therefore see fewer high-mass objects at high redshift than at low redshift.
Recent observations – I refer you to our paper for references – have revealed evidence for the existence of some very massive galaxy clusters at redshifts around unity or larger, which corresponds to a look-back time of greater than 7 Gyr. Actually these are not at high redshift compared to galaxies, which have bee found at redshifts around 10, where the lookback time is more like 12 Gyr, but these are at least a thousand times less massive than large clusters so their existence in the early Universe is not surprising in the framework of the standard cosmological model. On the other hand, clusters of the masses we’re talking about – about 1,000,000,000,000,000 times the mass of the Sun – should form pretty late in cosmic history so have the potential to challenge the standard theory.
In the paper we approach the issue in a different manner to other analyses and apply Extreme Value Statistics to ask how massive we would expect the largest cluster in the observable universe should be as a function of redshift. If we see one larger than the limits imposed by this calculation then we really need to consider modifying the standard theory. This way of tackling the problem attempts to finesse a number of biases in the usual approach, which is to attempt to estimate the number-density 
of clusters as a function of mass 
, because it does not require a correction for a posteori selection effects; it is not obvious, for example, prevcisely what volume is being probed by the surveys yielding these cluster candidates.
Anyway, the results are summarised in our Figure 1, which shows some estimated cluster masses, together with their uncertainties, superimposed on the theoretical distribution of the mass of the most massive cluster at that redshift:
If you’re wondering why the curves turn down at very low redshift, it’s just because the volume available to be observed at low redshift is small: although objects are generally more massive at low redshift, the chance of getting a really big one is reduced by the fact that one is observing a much smaller part of space-time.
The results show: (a) that, contrary to some claims, the current observations are actually entirely consistent with the standard concordance model; but also (b) that the existence of clusters at redshifts around 1.5 with masses much bigger than 
would require the tabling of an amendment to the standard theory.
Of course this is is a very conservative approach and it yields what is essentially a null result, but I take the view that while theorists should be prepared to consider radical new theoretical ideas, we should also be conservative when it comes to the interpretation of data.
In the Dark 