Scalar-multi-tensorial equivalence for higher order $f\left(R,{\nabla }_{\mu }R,{\nabla }_{{\mu }_1}{\nabla }_{{\mu }_2}R,...,{\nabla }_{{\mu }_1}...{\nabla }_{{\mu }_n}R\right)$ theories of gravity

R. R. Cuzinatto, C. A. M. de Melo, L. G. Medeiros +1

The equivalence between theories depending on the derivatives of $R$, i.e. $f\left(R,\nabla R,...,{\nabla }^{n}R\right)$, and scalar-multi-tensorial theories is verified. The analys…