Time evolution of the local gravitational parameters and gravitational wave polarizations in a relativistic MOND theory
Shuxun Tian, Shaoqi Hou, Shuo Cao, Zong‐Hong Zhu
Abstract
The recently proposed Skordis-Z\l{}o\ifmmode \acute{s}\else \'{s}\fi{}nik theory is the first relativistic modified Newtonian dynamics (MOND) theory that can recover the success of the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model at matching observations of the cosmic microwave background. This paper aims to revisit the Newtonian and MOND approximations and the gravitational wave analysis of the theory. For the local gravitational parameters, we show that one could obtain both time-varying effective Newtonian gravitational constant ${G}_{\mathrm{N}}$ and time-varying characteristic MOND acceleration scale ${a}_{\mathrm{MOND}}$, by relaxing the static assumption extensively adopted in the literature. Specially, we successfully demonstrate how to reproduce the redshift dependence of ${a}_{\mathrm{MOND}}$ observed in the nmagneticum cold dark matter simulations. For the gravitational waves, we show that there are only two tensor polarizations and reconfirm that its speed is equal to the speed of light.