Turnaround radius in $f(R)$ model
  We investigate the turnaround radius in the spherical collapse model, both in
General Relativity and in modified gravity, in particular $f(R)$ scenarios. The
phases of spherical collapse are marked by the density contrast in the instant
of turnaround $\delta_t$, and by the linear density contrast in the moment of
collapse, $\delta_c$. We find that the effective mass of the extra scalar
degree of freedom which arises in modified gravity models has an impact on
$\delta_t$ of up to $\sim10\%$, and that $\delta_c$ can increase by
$\sim1.0\%$. We also compute the turnaround radius, $R_t$, which in modified
gravity models can increase by up to $\sim 6\%$ at $z \simeq 0$.
