Equivalence between Palatini and metric formalisms of f(R)-gravity by divergence free current

Abstract

The equivalence between metric and Palatini formalisms in f(R)-gravity can be achieved in the general context of theories with divergence free current. This equivalence is a necessary result of a symmetry which is included in a particular conservation equation of the current. In fact the conservation equation, by an appropriate redefinition of the introduced auxiliary field, may be encoded in a massless scalar field equation.

6 pages

References in corpus (4)

• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• CMB and Matter Power Spectra of Early f(R) Cosmology in Palatini Formalism
• From Dark Energy and Dark Matter to Dark Metric
• Signature change, vacuum condensation and cosmological constant

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• Some aspects of modified theory of gravity in Palatini formalism unveiled
• Post-inflationary Leptogenesis and Dark Matter production: Metric versus Palatini formalism
• Classical and quantum cosmology in $f(T)$-gravity theory: A Noether symmetry approach