  A paper by Harmut Traunm\"uller [1] showed from statistical studies of
observational data that the most adequate equation to represent observations on
magnitude and redshift from 892 type 1a supernovae is $\mu =
5\,log[(1+z)\,ln(1+z)] + const.$ Comparing the Hubble diagram calculated from
the observed redshift data of 280 supernovae with Hubble diagrams inferred on
the basis of two cosmological models in the range of z = 0.0104 to 8.1, Laszlo
Marosi [2] found in a quite independant study that the best fit function to
represent observations is $\mu= 44.109769 \,z^{0.059883}$. Noting that
differences between the different cosmological models become more pronouced in
a photon time-of-fligth $t_s$ vs. $z$ repr\'esentation, he also noted that the
best equation to account for observations may also be written $z =
-1+e^{2.024\,\,10^{-18} \,\,ts}$. In the light of these observational data, we
compare the theoretical Hubble diagram obtained with the flat $\Lambda CDM$
model to the ones we have obtained few years ago [3, 4, 5] from a model that we
call here the "light model" for the sake of clarity. Our conclusions are that
values calculated on the basis of the $\Lambda CDM$ model exhibit poor
agreement with the presently available data while the light model agrees
exactly with observations and conclusions of statistical studies [1] and [2]
(independently of the values of $\Omega_k$, $\Omega_M$ or $\Omega_{\Lambda}$).
Our model giving no accelerating expansion of the universe, we conclude that
this latter is not necessary and that models can exist which lead exactly to
observations without having to consider any accelerating expansion of the
universe. In an Appendix, we discuss some aspects of the model and we present a
brief overview of some of its key results.
