A de Sitter $S$-matrix for the masses

We define an $S$-matrix for massive scalar fields on a fixed de Sitter spacetime, in the expanding patch co-ordinates relevant for early Universe cosmology. It enjoys many of the same properties as its Minkowski counterpart, for instance: it is insensitive to total derivatives and field redefinitions in the action; it can be extracted as a particular "on-shell" limit of time-ordered correlation functions; and for low-point scattering, kinematics strongly constrains its possible structures. We present explicit formulae relating the usual observables - in-in equal-time correlators and wavefunction coefficients at the conformal boundary - to $S$-matrix elements. Finally, we discuss some of the subtleties in extending this $S$-matrix to light fields (in the complementary series).