Extended Gravity

Abstract

We shall show equivalence between Palatini-$f(\calR)$ 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-$f(\calR)$ 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 lá 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.

References in corpus (6)

• On Physical Equivalence between Nonlinear Gravity Theories
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Universality of Einstein Equations for the Ricci Squared Lagrangians
• Re-examination of Polytropic Spheres in Palatini f(R) Gravity
• Matter Lagrangians Coupled with Connections
• Conformal Gravity with Electrodynamics for Fermion Fields and their Symmetry Breaking Mechanism

Cited by in corpus (6)

• A further study on Palatini f(R)-theories for polytropic stars
• Solar System Tests in Brans-Dicke and Palatini f(R)-theories
• The effective Equation of State in Palatini $f(R)$ cosmology
• Hubble drift in Palatini $f(\mathcal{R})$-theories
• Nonlinear Gravitational Lagrangians revisited
• Scalar-tensor gravity in the Palatini approach