Scattering of Quantum Particles in de Sitter Spacetime I: The Formalism

TL;DR

This paper develops a formalism for calculating quantum scattering amplitudes in de Sitter spacetime, linking quantum states to symmetry representations and showing how amplitudes relate to flat spacetime results.

Contribution

It introduces a new formalism for scattering in de Sitter space using symmetry group representations and generalizes Dyson's formula for this curved background.

Findings

Scattering amplitudes in de Sitter are given by a generalized Dyson's formula.

Wavepacket frequency spectra are geometry-dependent and narrow with larger masses or momenta.

Asymptotic de Sitter amplitudes match Minkowski spacetime results.

Abstract

We develop a formalism for computing the scattering amplitudes in maximally symmetric de Sitter spacetime with compact spatial dimensions. We describe quantum states by using the representation theory of de Sitter symmetry group and link the Hilbert space to geodesic observers. The positive and negative ``energy'' wavefunctions are uniquely determined by the requirement that in observer's neighborhood, short wavelengths propagate as plane waves with positive and negative frequencies, respectively; they define a unique ``Euclidean'' (a.k.a.\ Bunch-Davies) de Sitter invariant vacuum, common to all inertial observers. By following the same steps as in Minkowski spacetime, we show that the scattering amplitudes are given by a generalized Dyson's formula. Compared to the flat case, they describe the scattering of wavepackets with the frequency spectrum determined by geometry. The frequency spread shrinks as the masses and/or momenta become larger than the curvature scale. Asymptotically, de Sitter amplitudes agree with the amplitudes evaluated in Minkowski spacetime.