I Is the weak field limit valid for the Brans-Dicke scalar field?

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The Brans-Dicke theory is a scalar-tensor modification of general relativity that has been tested against solar system experiments which show that the parameter implying that the theory is almost indistinguishable from GR.

These tests assume the weak field limit of the theory so that the scalar field .

But is this valid if the scalar field is long range so that all the mass in the Universe at any distance contributes to at any given point in space?
 
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