On the time dependency of $a_0$

Abstract

In this paper, we test one of the predictions of the Scale Invariant Vacuum (SIV) theory on MOND. According to that theory, MOND's acceleration $a_0$ is not a universal quantity but depends on several parameters, including time. To check this prediction, we compare the dependency of $a_0$ from redshift, using the values of $a_0$ obtained in Marra et al. (2020) by carrying a Bayesian inference for 153 galaxies of the SPARC sample. Since this sample does not contain galaxies at large redshift, we have estimated $a_0$ from the data in Nestor Shachar et al. (2023). The SPARC sample, for small values of the redshift, in the redshift range $0.00032-0.032$ gives a correlation with $z$, while the Nestor Shachar et al. (2023) data, in the higher redshift range $0.5-2.5$ gives an anti-correlation with the redshift $z$. Both samples show a dependency of $a_0$ from $z$, although the uncertainties involved are large, especially for the high-redshift galaxies. The combined sample gives an overall correlation of $a_0$ with $z$. The different behavior at low and high redshift can be related to a change of the $a_0(z)$ with redshift, or to the lower precision with which the high-redshift value of $a_0$ are known.