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If we consider the lagrangian to have both geometric parts (Ricci scalar) and also a field, the action would take the form below:

\begin{equation}

S=\frac{1}{2\kappa}\int{\sqrt{-g} (\ R + \frac{1}{2} g^{\mu\nu} \partial_\mu \phi \partial_\nu \phi -V(\phi)\ )}

\end{equation}

which are the Einstein-Hilbert, the kinetic and the potential term respectively.

About the dimensions \begin{equation} [R]=L^{-2}\end{equation}, which is of course the curvature, so the other terms must have the same dimension.

How is this possible?

aren't they energy terms?

don't they have dimension of energy?!!!

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# Lagrangian and dimension

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