CBB was discovered some years after Albert Einstein died. It was not part of the original context in GRT.
https://www.researchgate.net/post/Do_objects_move_in_relation_to_space-time_in_GR?
Is CMB A Part Of GRT In The Present Context?
Strictly speaking CMB has never been officially incorporated into GR. The question is asking if researchers have opinions one way or the other.
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