Mattig's relation and dynamical distance indicators

TL;DR

This paper explores the relationship between the Mattig redshift method in Friedmann cosmology and classical dynamical distance indicators based on Newtonian gravity, emphasizing the conceptual correctness of deriving cosmological distances from redshift and velocity data.

Contribution

It clarifies the connection between cosmological distance measurement methods and classical dynamical indicators, highlighting the Newtonian analogy and the proper way to derive metric distances.

Findings

The Friedmann model has a Newtonian analogy.

Redshift-based distances can be conceptually derived from velocity and redshift.

Proper metric distance is crucial for accurate cosmological measurements.

Abstract

We discuss how the redshift (Mattig) method in Friedmann cosmology relates to dynamical distance indicators based on Newton's gravity (Teerikorpi 2011). It belongs to the class of indicators where the relevant length inside the system is the distance itself (in this case the proper metric distance). As the Friedmann model has Newtonian analogy, its use to infer distances has instructive similarities to classical dynamical distance indicators. In view of the theoretical exact linear distance-velocity law, we emphasize that it is conceptually correct to derive the cosmological distance via the route: redshift (primarily observed) --> space expansion velocity (not directly observed) --> metric distance (physical length in "cm"). Important properties of the proper metric distance are summarized.