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The Ostrogradsky instability of higher derivative Lagrangians is derived fromfirst principles using Control theory and Lyapunov Stability Analysis. Thisresult is then used to argue that Born-Infeld Lagrangians are viablemodifications of the Einstein-Hilbert action provided the action is varied inaccordance with the Palatini formalism, in contrast to the metric formalism.Finally, the Born-Infeld version of the FRW equations are derived and thecosmological dynamics is studied for matter dominated closed and openuniverses, and the results are compared with the usual cosmology.

Ostrogradsky instability and Born-Infeld modified cosmology in Palatini formalism