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Extended Gravity Theories and the Einstein-Hilbert Action

David Wands
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Abstract

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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David Wands. 1993-07-23. Extended Gravity Theories and the Einstein-Hilbert Action. https://doi.org/10.1088/0264-9381%2F11%2F1%2F025

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