Galaxy Clusters as a probe of early dark energy
  We study a class of early dark energy (EDE) models, in which, unlike in
standard dark energy models, a substantial amount of dark energy exists in the
matter-dominated era. We self-consistently include dark energy perturbations,
and show that these models may be successfully constrained using future
observations of galaxy clusters, in particular the redshift abundance, and the
Sunyaev-Zel'dovich (SZ) power spectrum. We make predictions for EDE models, as
well as LCDM for incoming X-ray (eROSITA) and microwave (South Pole Telescope)
observations. We show that galaxy clusters' mass function and the SZ power
spectrum will put strong constraints both on the equation of state of \de today
and the redshift at which EDE transits to present-day LCDM like behavior for
these models, thus providing complementary information to the geometric probes
of dark energy. Not including perturbations in EDE models leads to those models
being practically indistinguishable from LCDM. An MCMC analysis of future
galaxy cluster surveys provides constraints for EDE parameters that are
competitive with and complementary to background expansion observations such as
supernovae.
