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We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities.
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S. Weinberg, “Gravitation and Cosmology : Principles and Applications of the General Theory of Relativity,”
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M. Crisostomi, K. Koyama and G. Tasinato, “Extended Scalar-Tensor Theories of Gravity,” JCAP 1604
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C. de Rham and A. Matas, “Ostrogradsky in Theories with Multiple Fields,” JCAP 1606
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J. M. Ezquiaga, J. García-Bellido and M. Zumalacárregui, Phys. Rev. D 94
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