Einstein Hilbert action

[Das apashanka]

My question is why is the lagrangian density term in the action is equal to ricci scaler for gravitational field

 

[haushofer]

See e.g. Carroll's notes: it's the simplest scalar which contains up to second order derivatives of the metric. But maybe 'why' is the wrong question. We don't know 'why'. But it works.

 

[Orodruin]

It might be mentioned in this context that many theories of modified gravity instead put a general function $f(R)$. Of course, to recover GR you need $f(R) \simeq R$ to leading approximation.