A rectilinear plot of the luminosity distance versus redshift of slope of 14.65 where the luminosity distance is expressed in Gly (billion light years) was obtained in  using the redshift adjusted distance modulus
[1o] which is based on photon flux.
The luminosity distance is an important concept in cosmology as this is the distance measure obtained from supernovae data using the distance modulus
. The standard formula of the luminosity distance is [d.sub.L] = (1 + z) [d.sub.M] = [d.sub.M]/a, where [d.sub.L] is the luminosity distance and [d.sub.M] the comoving transverse distance [1, p.
In the upper panel of Figure 3, the distance modulus
, which is defined by [mu] = 5 [log.sub.10] [D.sub.L] - 5 with [D.sub.L] in parsecs, is plotted as a function of redshift; while in the lower panel of Figure 3, the distance modulus
difference between the measured SNeIa data and analytical results derived fromEq.
In the present study a redshift adjustment to the distance modulus
Both the standard candle and Tully-Fisher method rely on the distance modulus
. As shown below the distance modulus
gives a measure of LTDs and not Euclidean distances.