Spherical collapse model and cluster number counts in power law $f(T)$ gravity

We study the spherical collapse model (SCM) in the framework of spatially flat power law $f(T) \propto (-T)^{b}$ gravity model. We find that the linear and non-linear growth of spherical overdensities of this particular $f(T)$ model are affected by the power-law parameter $b$. Finally, we compute the predicted number counts of virialized haloes in order to distinguish the current $f(T)$ model from the expectations of the concordance $\Lambda$ cosmology. Specifically, the present analysis suggests that the $f(T)$ gravity model with positive (negative) $b$ predicts more (less) virialized objects with respect to those of $\Lambda$CDM.