Does Earth's motion through the CMB coincide with the FLWR metric?

[mitochan]

TL;DR

Does FLWR metric coordinate and CBR homogeneous coordinate where the Earth has proper speed of 0.0013 c coincide ? If so why ?

The Earth is moving with respect to the CBR at a speed of 390 kilometers per second, I read in the article https://www.scientificamerican.com/article/how-fast-is-the-earth-mov/. Does FLWR metric coordinate space coincides with integrated local FRs where CBR is homogeneous, and the Earth is moving with 390 km/sec = 0.0013 c on it ? If so does the coincidence of CBR homogeneity and FLWR metric space have any reason or just by chance ?

 

[PeterDonis]

Does FLWR metric coordinate space coincides with integrated local FRs where CBR is homogeneous, and the Earth is moving with 390 km/sec = 0.0013 c on it ?

If you are asking if an observer at rest at any spatial position in standard FRW coordinates would see the CMBR as isotropic (the same in all directions), the answer is yes.

If so does the coincidence of CBR homogeneity and FLWR metric space have any reason or just by chance ?

It's because the standard FRW coordinate chart is explicitly constructed so that the homogeneity and isotropy of the spacetime is directly reflected in the metric.

 

[anuttarasammyak]

Homogeneity and isotropy of spacetime is basic idea of FRW coordinate chart.
Homogeneity and isotropy of CMBR is observed not on the Earth but at rest in a coordinate, say CMBR coordinate. One comes from idea and the other comes from observation. Maybe we should be careful to say which could come from the other. I do not think CMBR is only one phenomena to show homogeneity and isotropy of the universe, so it cannot be a cause or source of the homogeneity and isotropy.

 

[mitochan]

Thanks.

 

[vanhees71]

Please, don't forget once more Lemaitre. He's in fact the one who predicted what's usually called Hubble expansion, and only because he published in a not so well-known French-speaking journal, he should not be forgotten. So it's FLRW metric!