Some Comments on Dynamical Character of Cosmological Constant and GUP

TL;DR

This paper explores the dynamical nature of the cosmological constant through a generalized uncertainty relation, proposing a GUP for the pair 'cosmological constant - space-time volume' based on quantum gravity considerations.

Contribution

It introduces a generalized uncertainty principle for the cosmological constant and space-time volume, extending previous work with a more natural and explicit derivation.

Findings

Derived explicit form of the GUP for the cosmological constant and volume.

Linked the uncertainty relation to Planck-scale physics and early universe conditions.

Discussed implications for quantum gravity and cosmology.

Abstract

In this paper the results obtained by Minic and his colleagues on the uncertainty relation of the pair "cosmological constant - volume of space-time", where cosmological constant is a dynamical quantity, are reconsidered and generalized proceeding from a more natural viewpoint. It is demonstrated that on the basis of simple and natural assumptions this relation may be understood with the help of the uncertainty relation for the pair "energy - time". Since the latter is generalized at Planck's scales (Early Universe)- GUP, the first one may be generalized in a similar way. This means that we can suggest GUP for the pair "cosmological constant - space-time volume". Here the relation is derived in the explicit form, and also some implications are considered.