Einstein-Scalar Theories

Question

I have used the below code for \phi^4 theories but it does not give correct answer.

    \partial{#}::PartialDerivative;
\delta{#}::Accent;
g^{\mu\nu}::Symmetric;
S:= \int{ \sqrt{-g} ( R+R \phi+1/2 g^{\mu\nu}\partial_{\mu}{\phi} \partial_{\nu}{\phi} -1/2 m^2 \phi^2- \lambda \phi^4) }{x};
rl:= \phi -> \delta{\phi}, V -> V' \delta{\phi};

How can i derive it?

\begin{equation}
S:= \int{ \sqrt{-g} ( R+R \phi+1/2 g^{\mu\nu}\partial{\mu}{\phi} \partial{\nu}{\phi}-1/2 m^2 \phi^2- \lambda \phi^4) }{x} \end{equation}

Comments

So far there is no question here... Do you have a question other than "solve this problem for me"?

Nonetheless, my suggestion would be: vary one field at the time.

Answer 1

You are messing with the variation. My suggestion is not to expect that the program solve the problem... it just helps you!

You have to do it the right way, find the field equations of a field at a time.