Recently I have read some papers in which the authors considered higher order lagrangians. For example, in this paper "A path integral leading to higher-order Lagrangians" by C.Acatrinei the higher order Lagrangians occurs somehow naturally from the path integral approach. I am considering this as an applications to scalar field dark matter/dark energy approach and effects on holography. Are there any physical principle that limits Lagrangians only to first order?

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    $\begingroup$ Higher order formulations have been discussed many times on Phys.SE, e.g. here, here and links therein. $\endgroup$ – Qmechanic Jan 16 '16 at 11:20