De Sitter scattering amplitudes in the Born approximation
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Abstract
We present a covariant framework to compute scattering amplitudes and potentials in
a de Sitter background. In this setting, we compute the potential of a graviton-mediated
scattering process involving two very massive scalars at tree level. Although the obtained
scattering potential reproduces the Newtonian potential at short distances, on Hubble-
size length scales it is affected by the constant curvature: effectively, it yields a repulsive
force at sub-Hubble distances. This can be attributed to the expansion of the de Sitter
universe. Beyond the de Sitter horizon, the potential vanishes identically. Hence, the
scattering amplitude unveils the geometric properties of de Sitter spacetime in a novel
and nontrivial way.
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SciPost physics, 13, 5, SciPost Foundation, Amsterdam, 2022, https://doi.org/10.21468/SciPostPhys.13.5.106