Cosmography of f(R) - brane cosmology
  Cosmography is a useful tool to constrain cosmological models, in particular
dark energy models. In the case of modified theories of gravity, where the
equations of motion are generally quite complicated, cosmography can contribute
to select realistic models without imposing arbitrary choices a priori. Indeed,
its reliability is based on the assumptions that the universe is homogeneous
and isotropic on large scale and luminosity distance can be "tracked" by the
derivative series of the scale factor a(t). We apply this approach to induced
gravity brane-world models where an f(R)-term is present in the brane effective
action. The virtue of the model is to self-accelerate the normal and healthy
DGP branch once the f(R)-term deviates from the Hilbert-Einstein action. We
show that the model, coming from a fundamental theory, is consistent with the
LCDM scenario at low redshift. We finally estimate the cosmographic parameters
fitting the Union2 Type Ia Supernovae (SNeIa) dataset and the distance priors
from Baryon Acoustic Oscillations (BAO) and then provide constraints on the
present day values of f(R) and its second and third derivatives.
