Ostrogradsky instability and Born-Infeld modified cosmology in Palatini formalism

TL;DR

This paper investigates the stability of higher derivative theories and demonstrates that Born-Infeld modifications of gravity are viable within the Palatini formalism, deriving cosmological equations and analyzing their implications for universe dynamics.

Contribution

It establishes the Ostrogradsky instability criteria using control theory and Lyapunov analysis, and applies these to validate Born-Infeld gravity in the Palatini approach with derived cosmological models.

Findings

Born-Infeld Lagrangians are stable in Palatini formalism

Derived modified Friedmann equations for Born-Infeld gravity

Compared cosmological dynamics with standard models

Abstract

The Ostrogradsky instability of higher derivative Lagrangians is derived 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 metric 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.