Spherical collapse and virialization in $f(T)$ gravities
  Using the classical top-hat profile, we study the non-linear growth of
spherically symmetric density perturbation and structure formation in $f(T)$
gravities. In particular, three concrete models, which have been tested against
the observation of large-scale evolution and linear perturbation of the
universe in the cosmological scenario, are investigated in this framework,
covering both minimal and nonminimal coupling cases of $f(T)$ gravities.
Moreover, we consider the virialization of the overdense region in the models
after they detach from the background expanding universe and turn around to
collapse. We find that there are constraints in the magnitude and occurring
epoch of the initial perturbation. The existence of these constraints indicates
that a perturbation that is too weak or occurs too late will not be able to
stop the expanding of the overdense region. The illustration of the evolution
of the perturbation shows that in $f(T)$ gravities, the initial perturbation
within the constraints can eventually lead to clustering and form structure.
The evolution also shows that nonminimal coupling models collapse slower than
the minimal coupling one.
