Evolution of spherical over-densities in tachyon scalar field model

We study the tachyon scalar field model in flat FRW cosmology with the particular potential ${\varphi }^{-2}$ and the scale factor behavior $a(t)=t^n$. We consider the spherical collapse model and investigate the effects of the tachyon scalar field on the structure formation in flat FRW universe. We calculate ${\delta }_c(z_c)$, $\lambda (z_c)$, $\xi (z_c)$, ${\mathrm{\Delta }}_V(z_c)$, $\log [\nu f(\nu )]$ and $\log [n(k)]$ for the tachyon scalar field model and compare the results with the results of EdS model and $\mathrm{\Lambda }CDM$ model. It is shown that in the tachyon scalar field model the structure formation may occur earlier, in comparison to the other models.