On the cosmological viability of the Hu-Sawicki type modified induced
  gravity
  It has been shown recently that the normal branch of a DGP braneworld
scenario self-accelerates if the induced gravity on the brane is modified in
the spirit of $f(R)$ modified gravity. Within this viewpoint, we investigate
cosmological viability of the Hu-Sawicki type modified induced gravity.
Firstly, we present a dynamical system analysis of a general $f(R)$-DGP model.
We show that in the phase space of the model, there exist three standard
critical points; one of which is a de Sitter point corresponding to
accelerating phase of the universe expansion. The stability of this point
depends on the effective equation of state parameter of the curvature fluid. If
we consider the curvature fluid to be a canonical scalar field in the
equivalent scalar-tensor theory, the mentioned de Sitter phase is unstable,
otherwise it is an attractor, stable phase. We show that the effective equation
of state parameter of the model realizes an effective phantom-like behavior. A
cosmographic analysis shows that this model, which admits a stable de Sitter
phase in its expansion history, is a cosmologically viable scenario.
