Physics Related with Co-moving Coordinate System

TL;DR

This paper derives the metric of an expanding universe with zero acceleration using a kinematic approach, revealing that photon red-shift depends on co-moving coordinates rather than the scale factor, aligning with observations.

Contribution

It introduces a novel perspective on photon red-shift in an expanding universe, emphasizing the role of co-moving coordinates over the scale factor's time dependence.

Findings

Red-shift depends on co-moving coordinates in zero-acceleration universe

Derived metric aligns with supernova luminosity-distance observations

Provides a kinematic derivation of universe expansion without acceleration

Abstract

We derive the metric of an expanding universe with zero accelerations by pure kinematic method. By doing so we expatiate physics related with co-moving coordinate system in details. The most important discovery or our study is, in an expanding universe with zero accelerations, the red-shift of photons from distance galaxies is determined by the co-moving coordinate of the source galaxy instead of the scale factor's time dependence. Our discovery is consistent with the current observed super-novaes's luminosity-distance v.s. red-shift relations.