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

Thread starter p78653
Start date Jan 9, 2025
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Scalar field

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The Brans-Dicke theory, a scalar-tensor modification of general relativity, has been validated through solar system experiments indicating a parameter value of ##\omega > 40000##, making it nearly indistinguishable from general relativity. These experiments rely on the assumption of the weak field limit, where the scalar field is expressed as ##\phi = \phi_0 + \xi##. A key question arises regarding the validity of this assumption if the scalar field has long-range effects, potentially influenced by mass throughout the Universe. The discussion highlights concerns about the implications of a long-range scalar field on the weak field limit. Overall, the validity of the weak field limit in the context of a long-range Brans-Dicke scalar field remains an open question.

Jan 9, 2025

p78653

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 ##\omega \gt 40000## implying that the theory is almost indistinguishable from GR.

These tests assume the weak field limit of the theory so that the scalar field ##\phi = \phi_0 + \xi##.

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

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