Scalar-multi-tensorial equivalence for higher order f(R , ∇ μ R , ∇ μ 1 ∇ μ 2 R , … , ∇ μ 1 … ∇ μ n R) theories of gravity

• Main Author: Medeiros, Léo Gouvêa
• Publication Date: 2016
• Other Authors: Cuzinatto, R.R, Melo, C.A.M., Pompeia, P.J.
• Format: Article
• Language: eng
• Source: Repositório Institucional da UFRN
• Download full: https://repositorio.ufrn.br/jspui/handle/123456789/29908
• topic: Scalar-multi-tensorial; Theories of gravity

The equivalence between theories depending on the derivatives of R,i.e. f(R,∇ R,…,∇nR), and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that f(R,∇R,…,∇nR) theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms ω0=0 and ω0=−32 for metric and Palatini formalisms respectively. This result is analogous to what happens for f(R) theories. It is worth 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 f(R,∇R,…,∇nR) theories to be written as scalar-multi-tensorial theories. Finally, some examples are studied and the comparison of f(R∇R,…,∇nR) theories to f (R,□R,…,□nR) theories is performed