Extended Gravity
Abstract
We shall show equivalence between Palatini- theories and Brans-Dicke (BD) theories at the level of action principles in generic dimension with generic matter coupling. We do that by introducing the Helmholtz Lagrangian associated to Palatini- theory and then performing frame transformations in order to recover Einstein frame and Brans-Dicke frame. This clarifies the relation among different formulations and the transformations among different frames. Additionally, it defines a formulation {\it a l\'a Palatini} for the Brans-Dicke theory which is dynamically equivalent to metric BD (unlike the standard Palatini-formulation of metric BD theory which are {\it not} dynamically equivalent). In conclusion we discuss interpretation of extended theories of gravitation and perspectives.
Cite
@article{arxiv.1403.7036,
title = {Extended Gravity},
author = {L. Fatibene and S. Garruto},
journal= {arXiv preprint arXiv:1403.7036},
year = {2014}
}