A Serendipitous Galaxy Cluster Survey with {\em XMM\/}
P.T.P. Viana (1,2), A.K. Romer (3), A.R. Liddle (4), R.G. Mann (5)
(1) Centro de Astrof\'{\i}sica da Universidade do Porto, Rua das Estrelas s/n, 4150 Porto, Portugal
(2) Departamento de Matem\'{a}tica Aplicada da Faculdade de Ci\^{e}ncias da Universidade do Porto, Portugal
(3) Physics Department, Carnegie Mellon University, Pittsburgh, PA15213, USA
(4) Astronomy Centre, University of Sussex, Brighton BN1 9QJ, UK
(5) Institute for Astronomy, University of Edinburgh, Royal Observatory,
Blackford Hill, Edinburgh, EH9 3NJ, UK

This contribution briefly describes a serendipitous galaxy cluster survey that we plan to conduct with the {\em XMM\/} X--ray satellite. We have modelled the expected properties of such a survey for three different cosmological models, using an extended Press--Schechter formalism, combined with a detailed characterisation of the expected capabilities of the EPIC camera on board {\em XMM\/}. We find that the number of clusters in the catalogue, as well as their redshift distribution, is strongly dependent on the cosmological parameter $\Omega_0$, and to a lesser extent also on $\Omega_\Lambda$, thus making the survey well suited to place tight constraints on the first and lead to a rough estimate of the second. The survey would also facilitate a variety of follow-up projects, including the quantification of evolution in the cluster X-ray luminosity--temperature relation, the study of high-redshift galaxies via gravitational lensing, follow-up observations of the Sunyaev-Zel'dovich effect and foreground analyses of cosmic microwave background maps.