On quantum corrections to geodesics in de-Sitter spacetime

TL;DR

This paper constructs a coordinate-independent wave-packet solution for a massive scalar field in de-Sitter space, analyzing its propagation and quantum effects depending on the mass-to-Hubble ratio.

Contribution

It introduces a new wave-packet solution in de-Sitter space that is coordinate-independent and relates to the quantum vacuum, analyzing its classical and non-classical propagation regimes.

Findings

Wave packet propagates like a point particle if M >> H

Wave packet exhibits non-classical behavior if M is comparable to H

Solution relates to the de-Sitter two-point function

Abstract

We find a coordinate-independent wave-packet solution of the massive Klein-Gordon equation with the conformal coupling to gravity in the de-Sitter universe. This solution can locally be represented through the superposition of positive-frequency plane waves at any space-time point, assuming that the scalar-field mass $M$ is much bigger than the de-Sitter Hubble constant $H$. The solution is also shown to be related to the two-point function in the de-Sitter quantum vacuum. Moreover, we study the wave-packet propagation over cosmological times, depending on the ratio of $M$ and $H$. In doing so, we find that this wave packet propagates like a point-like particle of the same mass if $M \ggg H$, but, if otherwise, the wave packet behaves highly non-classically.