It is shown that the standard cosmological parallax–distance formula , as found in the literature , including text-books on cosmology , requires a correction .
This correction arises from the fact that any chosen baseline in a gravitationally bound system does not partake in the cosmological expansion and therefore two ends of the baseline used by the observer for parallax measurements can not form a set of co-moving co-ordinates , contrary to what seems to have been implicitly assumed in the standard text-book derivation of the parallax distance formula .
At large redshifts , the correction in parallax distance could be as large as a factor of three or more , in the currently favoured cosmologies ( viz . \Omega _ { \Lambda } = 0.73 ,k = 0 ) .
Even otherwise , irrespective of the amount of corrections involved , it is necessary to have formulae bereft of any shortcomings .
We further show that the parallax distance does not increase indefinitely with redshift and that even the farthest observable point ( i.e. , at redshift approaching infinity ) will have a finite parallax value , a factor that needs to be carefully taken into account when using distant objects as the background field against which the parallax of a foreground object is to be measured .