The Robertson-Walker Metric in a Pseudo-Complex General Relativity

TL;DR

This paper explores the implications of pseudo-complex General Relativity on the Robertson-Walker metric, revealing a dynamic dark energy component linked to the universe's expansion rate.

Contribution

It introduces a pseudo-complex extension to the Robertson-Walker metric, showing how it leads to a variable dark energy component dependent on the universe's radius.

Findings

A pseudo-complexified energy-momentum tensor suggests a dynamic dark energy.

Consistency with a constant cosmological constant requires a non-changing Hubble parameter.

Abstract

We investigate the consequences of the pseudo-complex General Relativity within a pseudo-complexified Roberston-Walker metric. A contribution to the energy-momentum tensor arises, which corresponds to a dark energy and may change with the radius of the universe, i.e., time. Only when the Hubble function $H$ does not change in time, the solution is consistent with a constant $\Lambda$.