Quantum mechanics in de Sitter space

TL;DR

This paper explores the potential phenomenological effects of the extended uncertainty principle in de Sitter space, highlighting that such effects are extremely small but theoretically significant due to spacetime curvature.

Contribution

It investigates the implications of the extended uncertainty principle in de Sitter spacetime and assesses the magnitude of resulting corrections to quantum mechanics.

Findings

Corrections are proportional to the ratio of quantum system size to de Sitter radius

Effects are exceedingly small in practical experiments

Theoretical relevance of spacetime curvature effects in atomic physics

Abstract

We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.