# Generalized Lovelock gravity - General Relativity and Quantum Cosmology

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Abstract: In the Riemann geometry, the metric-s equation of motion for an arbitraryLagrangian is succinctly expressed in term of the first variation of the actionwith respect to the Riemann tensor if the Riemann tensor were independent ofthe metric. Let this variation be called the E-tensor. Noting that the E-tensorand equations of the motion for a general Lovelock gravity have the samedifferential degree, we define generalized Lovelock gravity as polynomialscalar densities constructed out from the Riemann tensor and its arbitrarycovariant derivatives such that they lead to the same differential degree forthe E-tensor and the metric-s equation of motion. We consider Lagrangiandensities which are functional of the metric and the first covariant derivativeof the Riemann tensor. We then present the first non-trivial examples of thegeneralized Lovelock gravity terms.

Author: ** Qasem Exirifard**

Source: https://arxiv.org/