de Sitter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math> matrix for the masses

We define an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi></a:math> matrix for massive scalar fields on a fixed de Sitter spacetime, in the expanding patch coordinates 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 formulas relating inflationary observables—namely in-in equal-time correlators and wavefunction coefficients at the conformal boundary—to these <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi></c:math> matrix elements. This new formalism will allow modern amplitude methods to be applied directly in cosmology and hence provide a wider range of more accurate theoretical predictions for upcoming sky surveys. Published by the American Physical Society 2024