http://arxiv.org/abs/1603.01563
The equivalence between theories depending on the derivatives of $R$, i.e. $f\left( R,\nabla R,…,\nabla^{n}R\right) $, and scalar-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that $f\left( R,\nabla R,…,\nabla^{n}R\right) $ theories are equivalents to 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. Furthermore, sufficient conditions are established for $f\left( R,\nabla R,…,\nabla^{n}R\right) $ theories to be written as scalar-tensorial theories. Finally, some examples are studied and the comparison of $f\left( R,\nabla R,…,\nabla^{n}R\right) $ theories to $f\left( R,\Box R,…\Box^{n}R\right) $ theories are performed.
R. Cuzinatto, C. Melo, L. Medeiros, et. al.
Tue, 8 Mar 16
31/83
Comments: 13 pages