Extended Gravity Theories and the Einstein-Hilbert Action

Details Extended Gravity Theories and the Einstein-Hilbert Action Extended Gravity Theories and the Einstein-Hilbert Action

1993-07-23

arxiv.org/abs/gr-qc/9307034v1

Class.Quant.Grav.11:269-280,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, Plain Latex, SUSSEX-AST-93/7-1

Scientific paper

10.1088/0264-9381/11/1/025

I discuss the relation between arbitrarily high-order theories of gravity and scalar-tensor gravity at the level of the field equations and the action. I show that $(2n+4)$-order gravity is dynamically equivalent to Brans-Dicke gravity with an interaction potential for the Brans-Dicke field and $n$ further scalar fields. This scalar-tensor action is then conformally equivalent to the Einstein-Hilbert action with $n+1$ scalar fields. This clarifies the nature and extent of the conformal equivalence between extended gravity theories and general relativity with many scalar fields.

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