The simple answer to this is question "No." Why should it? The observable Universe is finite so the number of clusters cannot grow exponentially indefinitely. Figure 2 shows the final version of the plot I showed during my talk with the cumulative number of clusters known with time. This illustrates the recent slowing of the number of clusters discovered and the increased lag between the detection and final publication of clusters.
Figure 2. The total number of clusters with X-ray detections known with time. The solid line marks the number detected or likely to be detected. The dotted line marks the detections published in the literature. The continuation above 40 AG is for an optimistic (solid) and pessimistic (dashed) assumption for the efficiency of XMM-Newton serendipitous surveys. The circles mark the number required for "Edge's Law" to hold.
As Simon White pointed out at the end of my talk, the case for ever-increasing sensitivity for the sake of it is a poor foundation for any field. The source counts for clusters crudely imply that every order of magnitude increase in number translates to an order of magnitude better sensitivity. So for the present, year 40 AG, the "Edge's Law" requirement would be equivalent to an all-sky survey to a flux of 10-13 erg s-1 cm-2 (0.5-2.0 keV). When I retire this will be 10-15 erg s-1 cm-2 (0.5-2.0 keV). This flux limit is reachable with current missions, but less than 1% of the sky could be covered.
There are, however, strong arguments for larger, deeper contiguous X-ray surveys than are available now or in the near future. The cosmological constraints that can be derived from the large-scale clustering of clusters, their mass function, and chemical evolution are complementary to those available elsewhere, most notably WMAP (Spergel et al. 2003). With the existence of large-area, multicolor optical and near-infrared surveys (e.g., SDSS, CHFTLS, RCS2, UKIDSS, Vista), the bottleneck of identification is eased and photometric redshifts will be sufficient for most purposes.
On a more practical level, the next generation of X-ray satellites, XEUS and Constellation-X, are optimized for the study of faint (10-14 erg s-1 cm-2) sources. To get the best from the massive investment made in these missions, it would be sensible to have surveyed more than 1% of the sky to this depth.
Several proposals have been made to do this and are listed in Table 3. To date none of these missions is fully approved. The case for DUET was based on a survey of the SDSS area (Jahoda et al. 2003) and would have detected 20,000 clusters. It is likely that a proposal of this type will succeed (probably ROSITA) so some form of all/part-sky survey will have been performed by 50-55 AG. It is very unlikely that any mission (proposed or yet to be proposed) is likely to reach the limits required to keep above "Edge's Law," but the constant progress made in X-ray astronomy will see the number of clusters increase to well above 30,000 by 60 AG. This should be sufficient for cosmological work and more detailed studies with the next generation of X-ray satellites.
|PANORAM-X||ESA Flexi Mission||rejected|
|ROSITA||ESA ISS Mission||accepted phase A, could fly 2007|