Physical Basis for the Symmetries in the Friedmann-Robertson-Walker Metric

TL;DR

This paper explores the physical origins of the symmetries in the FRW metric, revealing they are valid only for a medium with zero active mass, supported by observational data such as baryon acoustic oscillations.

Contribution

It derives the FRW metric coefficients from first principles and links the symmetries to the condition of zero active mass, providing a new physical understanding.

Findings

FRW symmetries are valid only for zero active mass media.

The derivation connects symmetries to free-fall co-moving frames.

Observational data supports the zero active mass condition.

Abstract

Modern cosmological theory is based on the Friedmann--Robertson--Walker (FRW) metric. Often written in terms of co-moving coordinates, this well-known solution to Einstein's equations owes its elegant and highly practical formulation to the cosmological principle and Weyl's postulate, upon which it is founded. However, there is physics behind such symmetries, and not all of it has yet been recognized. In this paper, we derive the FRW metric coefficients from the general form of the spherically symmetric line element and demonstrate that, because the co-moving frame also happens to be in free fall, the symmetries in FRW are valid only for a medium with zero active mass. In other words, the spacetime of a perfect fluid in cosmology may be correctly written as FRW only when its equation of state is rho+3p=0, in terms of the total pressure p and total energy density rho. There is now compelling observational support for this conclusion, including the Alcock--Paczynski test, which shows that only an FRW cosmology with zero active mass is consistent with the latest model-independent baryon acoustic oscillation data.