Elucidating the z-dependence of the MOND acceleration (a_0) within the Scale Invariant Vacuum (SIV) paradigm

Abstract: In a paper: On the time dependency of $a_0$" the authors claim that they have testedone of the predictions of the Scale Invariant Vacuum (SIV) theory on MOND" by studying the dependence of the Modified Newtonian Dynamics (MOND) acceleration at two data sets, low-$z$ ($$3.2\times10^{-4}\le z\le 3.2\times10<sup>{-2}$$) and high-$z$ ($0.5\le z\le 2.5$). They claim ``both samples show a dependency of $a_0$ from $z$". Here, the work mentioned above is revisited. The explicit analytic expression for the $z$-dependence of the $a_0$ within the SIV theory is given. Furthermore, the first estimates of the $\Omega_m$ within SIV theory give $\Omega_{m}=0.28\pm 0.04$ using the low-z data only, while a value of $\Omega_{m}=0.055$ is obtained using both data sets. This much lower $\Omega_m$ leaves no room for non-baryonic matter! Unlike in the mentioned paper above, the slope in the $z$-dependence of $A_0=\log_{10}(a_0)$ is estimated to be consistent with zero Z-slope for the two data sets. Finally, the statistics of the data are consistent with the SIV predictions; in particular, the possibility of change in the sign of the slopes for the two data sets is explainable within the SIV paradigm; however, the uncertainty in the data is too big for the clear demonstration of a $z$-dependence yet.