Physical basis for the symmetries in the Friedmann–Robertson–Walker metric
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, upo...
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| Language: | en |
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Springer Verlag
2016
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| Online Access: | http://hdl.handle.net/10150/614770 http://arizona.openrepository.com/arizona/handle/10150/614770 |
| Summary: | 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. |
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