Cosmological implications of the Gaia Milky Way declining rotation curve

Although the existence of dark matter has been widely acknowledged in the cosmology community, it is as yet unknown in nature, despite decades of research, which questions its very existence. This never-ending search for dark matter leads to consider alternatives. Since increasing the enclosed mass is the only way to explain the flat appearance of galaxies' rotation curves in a Newtonian framework, the MOND theory proposed to modify Newton's dynamics when the acceleration is around or below a threshold value, $a_0$. Observed rotation curves, generally flat at large distances, are then usually well reproduced by MOND with $a_0 \sim 1.2 10^{-10}$ m/s$^{2}$. However, the recent Gaia evidence of a decline in the Milky Way rotation curve is a distinct behavior. Therefore, we examine whether MOND can accommodate the Gaia declining rotation curve of the Milky Way. We first depict a standard model to describe the Milky Way's baryonic components. Secondly, we show that a NFW (Navarro, Frenk, \& White ) model is able to fit the decline, assuming a scale radius $R_s$ of the order of $4$ kpc. In a third step, we show that the usual MOND paradigm is not able to reproduce the declining part for a standard baryonic model. Finally, we examine whether the MOND theory can accommodate the declining part of the rotation curve when relaxing the characteristics of the baryonic components. To do so we use a MCMC method on the characteristics of the stellar and the HI disk, including their mass. We found that the stellar disk should be massive, of the order of $10^{11}$ M$_{\odot}$. The HI disk mass is capped at nearly 1.8 $10^{11}$ M$_{\odot}$ but could also be negligible. Finally, $a_0$ is consistent with 0, with an upper limit of $0.53 10^{-10}$ m/s$^{2}$ (95\%), a value much lower than the above mentioned value usually advocated to explain standard flat rotation curves in MOND theory.