  Recently, corrections to the standard Einstein-Hilbert action are proposed to
explain the current cosmic acceleration in stead of introducing dark energy. In
the Palatini formulation of those modified gravity models, there is an
important observation due to Arkani-Hamed: matter loops will give rise to a
correction to the modified gravity action proportional to the Ricci scalar of
the metric. In the presence of such term, we show that the current forms of
modified gravity models in Palatini formulation, specifically, the 1/R gravity
and $\ln R$ gravity, will have phantoms. Then we study the possible
instabilities due to the presence of phantom fields. We show that the strong
instability in the metric formulation of 1/R gravity indicated by Dolgov and
Kawasaki will not appear and the decay timescales for the phantom fields may be
long enough for the theories to make sense as effective field theory . On the
other hand, if we change the sign of the modification terms to eliminate the
phantoms, some other inconsistencies will arise for the various versions of the
modified gravity models. Finally, we comment on the universal property of the
Palatini formulation of the matter loops corrected modified gravity models and
its implications.
