Stability of Cosmological Solution in f(R) Models of Gravity

We reconcile seemingly conflicting statements in the literature about the behavior of cosmological solutions in modified theories of gravity where the Einstein-Hilbert Lagrangian for gravity is modified by the addition of a function of the Ricci scalar, f(R). Using the example of f(R) = +/-\mu^4/R we show that only such choices of f(R) where d^2f/dR^2>0 have stable high-curvature limits and well-behaved cosmological solutions with a proper era of matter domination. The remaining models enter a phase dominated by both matter and scalar kinetic energy where the scalar curvature remains low