Physical basis for the symmetries in the Friedmann–Robertson–Walker metric

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 principal and Weyl's postulate, upon which it is founded. But 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 {\it total} pressure $p$ and {\it total} energy density $\rho$. There is now compelling observational support for this conclusion, including the Alcock-Paczy\'nski test, which shows that only an FRW cosmology with zero active mass is consistent with the latest model-independent Baryon Acoustic Oscillation data.