Cosmological redshift, recession velocities and acceleration measures in FRW cosmologies

TL;DR

This paper analyzes how different measures of velocity and acceleration in FRW cosmologies relate to observable parameters, emphasizing the importance of synchronous reference frames and illustrating their behavior in the ΛCDM model.

Contribution

It provides a comprehensive discussion on velocity and acceleration measures in FRW cosmologies, including illustrative calculations and generalizations of the tethered galaxies problem.

Findings

Different velocity measures affect the interpretation of cosmic acceleration.

Apparent acceleration varies across epochs in the ΛCDM model.

Synchronous frames are crucial for understanding cosmological observations.

Abstract

In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker one is the most known example of them. We describe how different quantities behave in this frame. Special attention is paid to potentially observable parameters. We discuss different variants for choosing measures of velocity and acceleration representing the Hubble flow, and present illustrative calculations of apparent acceleration in flat $\Lambda CDM$ model for various epochs. We generalize description of the "tethered" galaxies problem for different velocity measures and equations of state, and illustrate time behavior of velocities and redshifts in the $\Lambda CDM$ model.