  Fourth - order gravity theories have received much interest in recent years
thanks to their ability to provide an accelerated cosmic expansion in a matter
only universe. In these theories, the Lagrangian density of the gravitational
field has the form R + f(R), and the explicit choice of the arbitrary function
f(R) must meet the local tests of gravity and the constraints from the
primordial abundance of the light elements. Two popular classes of f(R) models,
which are expected to fulfill all the above requirements, have recently been
proposed. However, neither of these models has ever been quantitatively tested
against the available astrophysical data. Here, by combining Type Ia Supernovae
and Gamma Ray Bursts, we investigate the ability of these models to reproduce
the observed Hubble diagram over the redshift range (0, 7). We find that both
models fit very well this dataset with the present day values of the matter
density and deceleration parameters which agree with previous estimates.
However, the strong degeneracy among the f(R) parameters prevents us from
putting strong constraints on the values of these parameters; nevertheless, we
can identify the regions of the parameter space that should, in principle, be
carefully explored with future data and dynamical probes in order to
discriminate among f(R) theories and standard dark energy models.
