New Exceptional Effective Field Theories in de Sitter Space from Generalized Energy Conservation

We discover a surprising relationship between exceptional effective field theories (EFTs) in de Sitter space and a notion of generalized energy conservation (GEC) of an S matrix defined in an extended Poincaré patch of four-dimensional de Sitter. By demanding that such an S matrix has support only when the total energies of in and out states are equal, we constrain the coupling constants in theories of self-interacting scalars living in the exceptional series of de Sitter representations. We rediscover the theories of Dirac-Born-Infeld (DBI) and special Galileon, and when increasing the conformal dimension, we find evidence for new exceptional theories where the four-point scalar self-interactions are uniquely fixed in terms of a single coupling constant. We conjecture that for each integer conformal dimension Δ≥4, there is at least one exceptional EFT that can be entirely fixed by GEC.