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تسجيل مستخدم جديدScalar-multi-tensorial equivalence for higher order $fleft( R, abla_{mu} R, abla_{mu_{1}} abla_{mu_{2}}R,..., abla_{mu_{1}}... abla_{mu_{n} }Rright)$ theories of gravity
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The equivalence between theories depending on the derivatives of $R$, i.e. $fleft( R, abla R,..., abla^{n}Rright) $, and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that $fleft( R, abla R,..., abla^{n}Rright) $ theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms $omega_{0}=0$ and $omega_{0}= - frac{3}{2}$ for metric and Palatini formalisms respectively. This result is analogous to what happens for $f(R)$ theories. It is worthy emphasizing that the scalar-multi-tensorial theories obtained here differ from Brans-Dicke ones due to the presence of multiple tensorial fields absent in the last. Furthermore, sufficient conditions are established for $fleft( R, abla R,..., abla^{n}Rright) $ theories to be written as scalar-multi-tensorial theories. Finally, some examples are studied and the comparison of $fleft( R, abla R,..., abla^{n}Rright) $ theories to $fleft( R,Box R,...Box^{n}Rright) $ theories is performed.
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In Cuzinatto et al. [Phys. Rev. D 93, 124034 (2016)], it has been demonstrated that theories of gravity in which the Lagrangian includes terms depending on the scalar curvature $R$ and its derivatives up to order $n$, i.e. $fleft(R, abla_{mu}R, abla_
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