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

## TL;DR

This paper revisits a relativistic MOND theory, demonstrating time-varying gravitational parameters and confirming the existence of only two tensor polarizations in gravitational waves, aligning with general relativity predictions.

## Contribution

It shows how to obtain time-varying Newtonian and MOND parameters by relaxing static assumptions and reproduces observed redshift dependence of MOND acceleration scale.

## Key findings

- Time-varying effective Newtonian constant $G_N$ and MOND acceleration scale $a_{MOND}$.
- Reproduction of redshift dependence of $a_{MOND}$ from simulations.
- Confirmation of two tensor polarizations and gravitational wave speed equal to light speed.

## Abstract

The recently proposed Skordis-Z\l{}o\'{s}nik theory is the first relativistic MOND theory that can recover the success of the standard $\Lambda$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 \textit{constant} $G_\textrm{N}$ and time-varying characteristic MOND acceleration scale $a_\textrm{MOND}$, by relaxing the static assumption extensively adopted in the literature. Specially, we successfully demonstrate how to reproduce the redshift dependence of $a_\textrm{MOND}$ observed in the \textit{Magneticum} 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.