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.