Cluster mass functions in the quintessential universe

We use N-body simulations to measure mass functions in flat cosmological models with quintessence characterized by constant w with w=-1, -2/3 and -1/2. The results are compared with the predictions of the formula proposed by Jenkins et al. at different redshifts, in terms of friends-of-friends (FOF) masses as well as Abell masses appropriate for direct comparison with observations. The formula reproduces quite well the mass functions of simulated haloes in models with quintessence. We use the cluster mass function data at a number of redshifts from Carlberg et al. to constrain Omega(0), sigma(8) and w. The best fit is obtained in the limit w-->0, but none of the values of w in the considered range -1less than or equal tow<0 can actually be excluded. However, the adopted value of w significantly affects the constraints in the Omega(0)-sigma(8) plane. Taking into account the dependence on w we find Omega(0)=0.32 +/- 0.15 and sigma(8)=0.85(-0.12)(+0.38) (68 per cent confidence level). Because less negative w push the confidence regions toward higher Omega(0) and lower sigma(8), we conclude that relaxing the assumption of w=-1, typically made in such comparisons, may resolve the discrepancy between recent cluster mass function results (yielding rather low Omega(0) and high sigma(8)) and most other estimates. The fact that high w values are preferred may, however, also point towards some unknown systematics in the data or the model with constant w being inadequate.