  Modifications to gravity that add additional functions of the Ricci curvature
to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have
been studied in great detail. When considered as complete theories of gravity
they can generate non-perturbative deviations from the general relativistic
predictions in the solar system, and the simplest models show instabilites on
cosmological scales. Here we show that it is possible to treat
$f(R)=R\pm\mu^4/R$ gravity in a perturbative fashion such that it shows no
instabilities on cosmological scales and, in the solar system, is consistent
with measurements of the PPN parameters. We show that such a theory produces a
spatially flat, accelerating universe, even in the absence of dark energy and
when the matter density is too small to close the universe in the general
relativistic case.
