Coupled Quintessence and the Halo Mass Function
  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 semi--analytic expressions for the 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 non--linear 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
$\Lambda$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 $\Lambda$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 $\Lambda$CDM.
