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Equation of motion for gravity in scalar-tensor theory
I'm trying to derive equation of motion in Higgs scalar-tensor theory with the Lagrangian given by
$$\mathcal{L}=[\frac{1}{16\pi}\alpha \phi^{\dagger}\phi R+ \frac{1}{2}\phi^{\dagger}_{;\mu}\phi^{;\mu}...
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Demonstration of the Brans-Dicke's Lagrangian
The Lagrangian in general relativity is written in the following form:
$$
\begin {aligned}
\mathcal {L} & = \frac {1} {2} g ^ {\mu \nu} \nabla_{\mu} \phi \nabla_{\nu} \phi-V (\phi) \\
& = R + \...
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