Abstract
Within the framework of extended theories of gravitation we shall discuss physical equivalences among di erent formalisms and classical tests. As suggested by the Ehlers-Pirani-Schild framework, the conformal invariance will be preserved and its e ect on observational protocols discussed. Accordingly, we shall review standard tests showing how Palatini f (R)-theories naturally passes solar system tests. Observation pro- tocols will be discussed in this wider framework.
Highlights
In [1] we defined and discussed extended theories of gravitation (ETG) and their EPS interpretation; see [2], [3]
In particular we shall show that Palatini f (R)-theories are mathematically equivalent to Brans-Dicke theories, they are physically inequivalent being free fall different in the two theories
We reviewed the equivalence with Brans-Dicke models though we argued that the mathematical equivalence does not extend to a physical equivalence between the two models
Summary
In [1] we defined and discussed extended theories of gravitation (ETG) and their EPS interpretation; see [2], [3]. In particular we introduced Palatini f (R)-theories in which one considers as fundamental fields a metric g, a (torsionless) connection Γtogether with a collection of matter fields ψ; see [4], [5],. The triple (M, [g], Γ = {g}) is an integrable Weyl geometry on spacetime By observing field equations (2) one can see how Palatini f (R)-theories behave like standard GR, but with a different effective source term Tμν. In particular we shall show that Palatini f (R)-theories are mathematically equivalent to Brans-Dicke theories (which are ruled out by classical tests in the Solar System), they are physically inequivalent being free fall different in the two theories. We refer to the appendix for a discussion in a simple mechanical example about how observables can violate mathematical equivalence
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