Title: A Correction in the Cosmological Parallax--Distance Formula Authors: Ashok K. Singal

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 cannot 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.