Clustering of dark matter in interacting tachyon dark energy with
  $\Lambda$CDM background
  One of the non-canonical descriptions of scalar field dark energy is the
tachyon. The present work is devoted to study the dynamics of dark matter
overdensity in a conformally coupled tachyon field dark energy model. The model
is tuned to mimic the $\Lambda$CDM cosmology at background level. The
semi-analytic spherical collapse model of dark matter overdensity is adopted to
study the nonlinear evolution. The effects of non-minimal coupling in the
energy budget on the clustering of dark matter is investigated. It is observed
that the growth rate of matter overdensity is higher in presence of the
non-minimal coupling. The critical density at collapse is suppressed in case of
interaction. Further the number counts of dark matter halos or galaxy clusters
along redshift are studied using the Press-Schechter and Sheth- Tormen halo
mass functions. Suppression in the number of dark matter halos is observed when
the interaction is allowed. A comparison of cluster number count in the present
model and $\Lambda$CDM is carried out. The present model allowing the
interaction produces much lower number of galaxy clusters compared to
$\Lambda$CDM, but without interaction the cluster number count is slightly
higher than $\Lambda$CDM cluster count.
