Galileons as the Scalar Analogue of General Relativity

Understand

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.