I Einstein Hilbert action

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    Einstein Hilbert
Das apashanka
My question is why is the lagrangian density term in the action is equal to ricci scaler for gravitational field
 
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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.
 
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.
 

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