Ostrogradsky instability and Born-Infeld modified cosmology in Palatini formalism
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AbstractThe Ostrogradsky instability of higher derivative Lagrangians is de-rived from first principles using Control theory and Lyapunov Stability Analysis. This result is then used to argue that Born-Infeld Lagrangians are viable modifications of the Einstein-Hilbert action provided the action is varied in accordance with the Palatini formalism, in contrast to the met-ric formalism. Finally, the Born-Infeld version of the FRW equations are derived and the cosmological dynamics is studied for matter dominated closed and open universes, and the results are compared with the usual cosmology.