Scalar-multi-tensorial equivalence for higher order f( R,∇_μ R,∇_μ₁∇_μ₂R,...,∇_μ₁...∇_μ_n R) theories of gravity

2016/03/31 by R. R. Cuzinatto, C. A. M. de Melo, L. G. Medeiros +1 · 1 citation
Physics and Astronomy · Mathematics · #gr-qc #astro-ph.CO #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevd.93.124034

published as Phys. Rev. D 93, 124034 (2016) · 12 pages, minor corrections

arxiv created 2018/06/21 · arxiv updated 2018/06/25

Abstract

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= - (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 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,\Box R,...\BoxⁿR) theories is performed.

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