We explain how one can recast cosmological correlators for conformally coupled $\phi^4$ theory in four-dimensional de Sitter space as flat space Feynman integrals. We evaluate the one-loop cosmological four-point functions in de Sitter space in terms of single-valued multiple polylogarithms.
We discuss a regularization which preserves de Sitter-invariance, which makes the flat space limit subtle to define at loop-level. Still, we find that up to two loops, the in-in correlators are structurally simpler than the wave function and have the same transcendentality as flat space amplitudes, and can be derived from a novel recursion relation.
