Cosmographic constraints on a class of Palatini f(R) gravity
  Modified gravity, known as $f(R)$ gravity, has presently been applied to
Cosmology as a realistic alternative to dark energy. For this kind of gravity
the expansion of the Universe may accelerate while containing only baryonic and
cold dark matter. The aim of the present investigation is to place cosmographic
constraints on the class of theories of the form $f(R)=R - \alpha/R^n$ within
the Palatini approach. Although extensively discussed in recent literature and
confronted with several observational data sets, cosmological tests are indeed
inconclusive about the true signal of $n$ in this class of theories. This is
particularly important to define which kind of corrections (infra-red or
high-energy) to general relativity this class of theory indeed represent. We
shed some light on this question by examining the evolution of the deceleration
parameter $q(z)$ for these theories. We find that for a large range of
$\alpha$, models based on $f(R) = R - \alpha/R^{n}$ gravity in the Palatini
approach can only have positive values for $n$, placing thus a broad
restriction on this class of gravity.
