A sufficiently light scalar field slowly evolving in a potential can account for the dark energy that presently dominates the Universe. This quintessence field is expected to couple directly to matter components, unless some symmetry of a more fundamental theory protects or suppresses it. Such a coupling would leave distinctive signatures in the background expansion history of the Universe and on cosmic structure formation, particularly at galaxy cluster scales. Using semianalytic expressions for the cold dark matter (CDM) halo mass function, we make predictions for halo abundance in models where the quintessence scalar field is coupled to cold dark matter, for a variety of quintessence potentials. We evaluate the linearly extrapolated density contrast at the redshift of collapse using the spherical collapse model and we compare this result to the corresponding prediction obtained from the nonlinear perturbation equations in the Newtonian limit. For all the models considered in this work, if there is a continuous flow of energy from the quintessence scalar field to the CDM component, then the predicted number of CDM haloes can only lie below that of $\Lambda \mathrm{CDM}$, when each model shares the same cosmological parameters today. In the last stage of our analysis we perform a global MCMC fit to data to find the best fit values for the cosmological model parameters. We find that for some forms of the quintessence potential, coupled dark energy models can offer a viable alternative to $\Lambda \mathrm{CDM}$ in light of the recent detections of massive high-$z$ galaxy clusters, while other models of coupled quintessence predict a smaller number of massive clusters at high redshift compared to $\Lambda \mathrm{CDM}$.

• Received 10 March 2011

DOI:https://doi.org/10.1103/PhysRevD.85.023503