Extended uncertainty principle and the geometry of (anti)-de Sitter space

TL;DR

This paper derives a modified uncertainty principle on (anti)-de Sitter space from its geometric properties, linking it to extended generalized uncertainty principles and triply special relativity.

Contribution

It provides a geometric derivation of the extended uncertainty principle in (anti)-de Sitter space and explores its relation to triply special relativity.

Findings

Modified uncertainty principle includes a term with the cosmological constant.

Geometric derivation from (anti)-de Sitter spacetime properties.

Connection established between extended GUP and triply special relativity.

Abstract

It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.