Borrowing inspiration from double field theory, one can write the Einstein-Hilbert term in variables which make two copies of Lorentz invariance manifest. This is achieved using a judicious local, invertible field redefinition and gauge choice. The resulting action resembles a nonlinear sigma model, is simpler to work with than the conventional metric formulation, and can be written on both flat and curved backgrounds.

One of the hopes in writing the action with a manifest twofold symmetry is that it will naturally explain the douple copy relations between gauge theory and gravity, i.e. that gravity scattering amplitudes are the square of gauge theory amplitudes.

The recent categorization of scalar EFTS according to their soft behaviour is extended to the case of theories with distinct power counting parameters. One recovers the same special cases of enhanced soft symmetry (namely the Galileons), and can verify that they are correctly related by the DBI galileon duality.

This is an important extension of the soft classification of scalar EFTs because it establishes that different theories with similar soft behaviour can be combined and retain their enhanced soft symmetry.