Wavepackets on de Sitter spacetime: first step towards a Haag-Ruelle scattering theory
In this colloquium, we want to present the first steps of the formulation of a scattering theory on a curved spacetime, in the Haag-Ruelle approach. This approach determines the S-matrix without specifying a particular interaction, it is rather based on the asymptotic behaviour of massive solutions of the wave equation, which can be estimated with great generality. We will show the construction of wavepackets on de Sitter spacetime, whose masses are consistently defined from the structure of the Lorentz algebra, and estimate its asymptotic behaviour. Furthermore, we show that, in the limit as the de Sitter radius tends to infinity, the wavepackets tend to the wavepackets of Minkowski spacetime and the plane waves arising after contraction have support sharply located on the mass shell. We will also show how to construct (scalar) field operators from these wavepackets. Besides, we will argue that the equilibrium state is not a thermal state, thus avoiding known issues of scattering theory at finite temperatures, and we will discuss possible interpretations of the in- and out-states.