T. Gayoux, P.-S. Corasaniti, T. R. G. Richardson, S.T. Kay, A. M. C. Le Brun, L. Moscardini, L. Pizzuti, S. Bocquet, S. Borgani, M. Costanzi, C. Giocoli, S. Grandis, A. Ragagnin, J. Rhodes, I. Sáez-Casares, M. Sereno, E. Sarpa, B. Altieri, A. Amara, S. Andreon, N. Auricchio, C. Baccigalupi, M. Baldi, S. Bardelli, A. Biviano, E. Branchini, M. Brescia, S. Camera, G. Cañas-Herrera, V. Capobianco, C. Carbone, J. Carretero, S. Casas, M. Castellano, G. Castignani, S. Cavuoti, K. C. Chambers, A. Cimatti, C. Colodro-Conde, G. Congedo, L. Conversi, Y. Copin, F. Courbin, H. M. Courtois, A. Da Silva, H. Degaudenzi, G. De Lucia, H. Dole, F. Dubath, C. A. J. Duncan, X. Dupac, S. Dusini, S. Escoffier, M. Farina, R. Farinelli, S. Farrens, F. Faustini, S. Ferriol, F. Finelli, M. Frailis, E. Franceschi, M. Fumana, S. Galeotta, K. George, B. Gillis, J. Gracia-Carpio, A. Grazian, F. Grupp, S. V. H. Haugan, W. Holmes, F. Hormuth, A. Hornstrup, K. Jahnke, M. Jhabvala, E. Keihänen, S. Kermiche, A. Kiessling, M. Kilbinger, B. Kubik, M. Kunz, H. Kurki-Suonio, O. Lahav, S. Ligori, P. B. Lilje, V. Lindholm, I. Lloro, G. Mainetti, D. Maino, E. Maiorano, O. Mansutti, S. Marcin, O. Marggraf, M. Martinelli, N. Martinet, F. Marulli, R. J. Massey, E. Medinaceli, S. Mei, Y. Mellier, M. Meneghetti
The large catalogues of galaxy clusters expected from the Euclid survey will enable cosmological analyses of cluster number counts that require accurate cosmological model predictions. One possibility is to use parametric fits calibrated against N-body simulations, which capture the cosmological parameter dependence of the halo mass function (HMF). Several studies have shown that this can be obtained through a calibration against haloes with spherical masses defined at the virial overdensity. In contrast, if different mass definitions are used for the HMF and the mass-observable relation, a mapping between them is required. Here, we investigate the impact of such a mapping on the cosmological parameter constraints inferred from galaxy cluster number counts for a fiducial Λ cold dark matter cosmology. Using synthetic data from N-body simulations, we show that the standard approach, which relies on assuming a concentration-mass relation, can introduce significant systematic bias. In particular, depending on the halo mass definition and the concentration-mass relation assumed, this can lead to biased constraints at a level of more than 2σ. In contrast, we find that in all the cases we have considered, the mass conversion based on the halo sparsity statistics results in a systematic bias that is smaller than the statistical error.