Instabilities in modified theories of gravity

Superpotential method for $F(R)$ cosmological models

“…For example, the Starobinsky R 2 inflationary model [4] (see also [5]) leads to the predictions that do not contradict to the observation data [6]. Dark energy F (R) models are actively investigated and analyzed, for example, in papers [7,8,9,10,11,12,13,14,15]. Moreover, there are F (R) gravity models that can describe both inflation and the late time cosmic acceleration [16,17,18].…”