  Context. One science goal of the upcoming Planck mission is to perform a
full-sky cluster survey based on the Sunyaev-Zel'dovich (SZ) effect, which
leads to the question of how such a survey would be affected by cosmological
models with a different history of structure formation than LCDM. One class of
these models are early dark energy (EDE) cosmologies, where the dark energy
contribution does not vanish at early times.
  Aims. Since structures grow slower in the presence of EDE, one expects an
increase in the number of galaxy clusters compared to LCDM at intermediate and
high redshifts, which could explain the reported excess of the angular CMB
power spectrum on cluster scales via an enhanced SZ contribution. We study the
impact of EDE on Planck's expected cluster sample.
  Methods. To obtain realistic simulations, we constructed full-sky SZ maps for
EDE and LCDM cosmologies, taking angular cluster correlation into account.
Using these maps, we simulated Planck observations with and without Galactic
foregrounds and fed the results into our filter pipeline based on the spherical
multi-frequency matched filters.
  Results. For the case of EDE cosmologies, we clearly find an increase in the
detected number of clusters compared to the fiducial LCDM case. This shows that
the spherical multi-frequency matched filter is sensitive enough to find
deviations from the LCDM sample, being caused by EDE. In addition we find an
interesting effect of EDE on the completeness of the cluster sample, such that
EDE helps to obtain cleaner samples.
