Cosmological dynamics of fourth-order gravity: A compact view

We construct a compact phase space for flat Friedmann-Lemaitre-Robertson-Walker spacetimes with standard matter described by a perfect fluid with a barotropic equation of state for general f(R) theories of gravity, subject to certain conditions on the function f. We then use this framework to study the behavior of the phase space of universes with a non-negative Ricci scalar in R + alpha R-n Rn gravity. We find a number of interesting cosmological evolutions which include the possibility of an initial unstable power-law inflationary point, followed by a curvature-fluid-dominated phase mimicking standard radiation, then passing through a standard matter era and ultimately evolving asymptotically towards a de Sitter-like late-time accelerated phase.