A Redshift-Magnitude Relation for Non-Uniform Pressure Universes

TL;DR

This paper derives a redshift-magnitude relation for non-uniform pressure Stephani universes, highlighting how spatial pressure variations influence observational cosmology and offering potential explanations for discrepancies with Friedman models.

Contribution

It presents the first-order redshift-magnitude relation in Stephani universes considering spatial pressure variations and explores observational implications for non-uniform pressure cosmologies.

Findings

Redshift-magnitude relation is direction-independent for central observers.

Spatial pressure effects mimic the deceleration parameter in Friedman models.

Angular dependence of the relation can explain observational discrepancies.

Abstract

A redshift-magnitude relation for the two exact non-uniform pressure spherically symmetric Stephani universes is presented. The Kristian-Sachs method expanding the relativistic quantities in series is used, but only first order terms in redshift $z$ are considered. The numerical results are given both for centrally placed and non-centrally placed observers. In the former case the redshift-magnitude relation does not depend on the direction in the sky and the Friedman limit can be easily performed. It appears that the effect of spatial dependence of pressure is similar to the effect of the deceleration parameter in Friedman models. In the latter case the angular dependence of the relation is important. This may serve as another possible explanation of the non-compatibility of the theoretical curve of the redshift-magnitude relation with observations for large redshift objects in the Friedman universe. On the other hand, comparing the magnitudes of equal redshifts objects in different directions in the sky, one can test the reliability of these models.