As I know that the definition of the CMB rest frame is the comoving frame of the plasma emitting CMB. And the anisotropy of CMB is due to the velocity difference between the earth frame and the CMB frame. But I have read a textbook mentioning that observers are at rest with the current CMB proper frame and a star at $z$ should be at rest with the CMB proper frame at $z$. What is the meaning of "current" CMB proper frame?
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