Time evolution of the local gravitational parameters and gravitational wave polarizations in a relativistic MOND theory

The recently proposed Skordis-Z\l{}o\'{s}nik theory is the first relativistic MOND that can recover success of standard $\Lambda$CDM model at matching observations cosmic microwave background. This paper aims to revisit Newtonian and approximations gravitational wave analysis theory. For local parameters, we show one could obtain both time-varying effective \textit{constant} $G_\textrm{N}$ characteristic acceleration scale $a_\textrm{MOND}$, by relaxing static assumption extensively adopted in literature. Specially, successfully demonstrate how reproduce redshift dependence $a_\textrm{MOND}$ observed \textit{Magneticum} cold dark matter simulations. waves, there are only two tensor polarizations, reconfirm its speed equal light.