Background cosmological dynamics in $f(R)$ gravity and observational constraints

In this paper, we carry out a study of viable cosmological models in $f(R)$-gravity at the background level. We use observable parameters like $\Omega$ and $\gamma$ to form autonomous system of equations and show that the models under consideration exhibit two different regimes in their time evolution, namely, a phantom phase followed by a quintessence like behavior. We employ statefinder parameters to emphasize a characteristic discriminative signature of these models.