The upcoming XMM Large Scale Structure Survey (XMM-LSS) will ultimately provide a unique mapping of the distribution of X-ray sources in a contiguous 64 sq. deg. region. In particular, it will provide the 3-dimensional location of about 900 galaxy clusters out to a redshift of about 1. We study the prospects that this cluster catalogue offers for measuring cosmological parameters. We use the Press-Schechter formalism to predict the counts of clusters and their X-ray properties in several CDM models. We compute the detection efficiency of clusters, using realistic simulations of XMM X-ray images, and study how it differs from a conventional flux limit. We compute the expected correlation function of clusters using the extended halo model, and show that it is expected to evolve very little out to z~2, once the selection function of the survey is taken into account. The shape and the amplitude of the correlation function can be used to brake degeneracies present when cluster counts alone are considered. Ignoring systematic uncertainties, the combination of cluster counts evolution and of the correlation function yields measurements of Omega_m, sigma_8 and Gamma with a precision of about 15%, 10% and 35%, respectively, in a LCDM model. This combination will also provide a consistency check for the LCDM model, and a discrimination between this model and the OCDM model. The XMM-LSS will therefore provide important constraints on cosmological parameters, complementing that from other methods such as the Cosmic Microwave Background. We discuss how these constraints are affected by instrumental systematics and by the uncertainties in the scaling relations of clusters.
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