= Brans-Dicke theory
{c}
{title2=$\mathcal L_g=\Phi R+\omega\Phi^{-1}(\nabla\Phi)^2$}
{wiki=Brans–Dicke_theory}
The <Brans-Dicke theory> adds a dynamical <scalar field> $\Phi$ to a <metric tensor> theory of gravity, with constant dimensionless coupling $\omega$. In a $(+---)$ signature and the reversed-curvature convention used here, the displayed Lagrangian is supplemented by matter and integrated against the <metric tensor> volume density with prefactor $1/(16\pi G)$. Its <scalar> multiplier of the <Ricci scalar> lets the <curvature> coupling vary in spacetime. Both the <metric tensor> and <scalar> are varied; the <scalar equation of Brans-Dicke theory> follows by eliminating <curvature> between the <scalar> equation and the <trace> of the <metric tensor> equation. The original construction is described in https://doi.org/10.1103/PhysRev.124.925[Brans and Dicke's 1961 article].
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