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Oct 28, 2021 at 22:39 comment added benrg He uses "redshift" to mean measured redshift, and "time dilation" to mean the ratio of measured duration to assumed proper duration. FLRW cosmology predicts that they're equal (if we have the proper duration right), but tired light predicts that they're different. The answer says "it appears that [he] is using gravitational time dilation as another term for gravitational redshift." That's incorrect as he never uses either term. If you delete "gravitational", it's still incorrect, because he's comparing different models, some of which distinguish the two.
Oct 28, 2021 at 20:06 comment added Dale Gravitational time dilation is $dt/d\tau$ for a worldline that is at rest in some specified coordinates (which obviously must include a time coordinate, $t$). When Wright discussed “time dilation” of comoving observers that would be gravitational time dilation in standard FLRW coordinates.
Oct 28, 2021 at 18:44 comment added benrg I don't understand this answer. Wright never uses the terms "gravitational time dilation" or "gravitational redshift" on the pages linked by OP, or in the passages you quoted. He uses "time dilation" and "redshift", but why would it be surprising that he uses those terms in more than one way? Everybody does.
Oct 28, 2021 at 17:12 comment added Dale Thank you. That is just referring to the OP's equation for FLRW spacetime that $d\tau=dt$ for all of the spatial variables constant. That indicates that there is no time dilation as a function of location in the FLRW spacetime, i.e. no gravitational time dilation.
Oct 28, 2021 at 16:40 comment added Árpád Szendrei Really nice answer. Can you please elaborate on this "there is no gravitational time dilation in the cosmological spacetime"?
Oct 28, 2021 at 11:26 history answered Dale CC BY-SA 4.0