  We establish a correspondence between general relativity with diffeomorphism
invariance and scalar field theories with Galilean invariance: notions such as
the Levi-Civita connection and the Riemann tensor have a Galilean counterpart.
This suggests Galilean theories as the unique nontrivial alternative to gauge
theories (including general relativity). Moreover, it is shown that the
requirement of first-order Palatini formalism uniquely determines the Galileon
models with second-order field equations, similar to the Lovelock gravity
theories. Possible extensions are discussed.
