Is general relativity the simplest possible theory of gravitation? I can't find this, but i've seen that GR  is the only possible theory of gravity if you assume causality and principle of equivalence?
 A: I guess, one of the simplest, if not the simplest theory of gravitation is Nordström's scalar theory that fulfils the weak equivalence principle with the field equation ($T$ is the trace of the enery-momentum tensor of matter):
$\phi \Box \phi = - 4\pi T$
It also fulfils causality as it is Lorentz-invariant. Even Einstein was at the beginning attracted by this theory, but nevertheless it has a couple of flaws:
It does not predict any deflection of light at massive bodies as the sun. Moreover, its prediction of the perihelion precession of Mercury is wrong. So it is not an acceptable theory, however it served as an intermediate step to General Relativity.
At the beginning Nordström even proposed a simpler theory, but I think, that one does not comply with the equivalence principle.
A: While Mr. Thomas's answer is correct, the simplest theory we have found that accounts for all observed phenomenon is GR, in the sense that its field equations are derived from the simplest possible Lagrangian. In curved space, the action takes the form $$S=\int d^nx\mathcal{L}=\int d^nx\sqrt{-g}\hat{\mathcal{L}}$$ where $\hat{\mathcal{L}}$ is a scalar. We want to pick the simplest possible scalar that is at least constructed from second derivatives of the metric (because the metric can be set to canonical form at each point of the manifold, so the first derivatives vanish). Any nontrivial tensor made from products of the metric and its first and second derivatives can be expressed in terms of the metric and Riemann tensor and the Ricci scalar is the only independent scalar we can construct from the Riemann tensor. Based on this, Hilbert originally proposed the simplest possible $\hat{\mathcal{L}}$ is simply $R$. Thus, we have the Hilbert action  $$S_H=\int d^nx R\sqrt{-g}$$
which produces the Einstien Field Equations. Thus, in this sense, GR really is the simplest possible theory, as it derives from the simplest possible Lagrangian.
