On the simplicity of de Sitter correlators

Motivated by recent evidence that equal-time correlators can be simpler than the corresponding wavefunction coefficients, we study de Sitter correlators in conformally coupled $\phi^3$ theory directly. By inverting the momentum-space dressing rules, we derive a time integral representation for generic graphs and show that its natural building blocks are flat space correlators of fields and conjugate momenta. Among other things, this representation gives two useful recursive structures, one obtained by collapsing leaves and one by fusing lower-point graphs. In this representation several simplifications also become immediate. Graphs with an odd number of conjugate momentum insertions vanish, explaining the weight drop of odd-point correlators, melonic insertions collapse to lower complexity graphs and the leading behavior near total and partial-energy singularities is manifest, closely paralleling the flat space story. We then take a first step beyond the integrand and study integrated answers. For tree level families, in particular chains and stars, we find that the symbol alphabet of the correlator is smaller than that of the corresponding wavefunction, with the missing letters admitting a natural interpretation in terms of tubing data. These results support a correlator-first viewpoint for de Sitter observables: part of their simplicity appears to be intrinsic to the correlator itself, rather than inherited indirectly from the wavefunction.