Gravitational wave birefringence in symmetron cosmology

The symmetron is a light scalar which provides a screening mechanism so as to evade the strong constraints from local gravity tests. To achieve this goal, a ${Z}_{2}$ symmetry is imposed on the symmetron model. In this paper, we introduce a new symmetron Chern-Simons-like gravitational interaction which is ${Z}_{2}$ invariant but breaks the parity symmetry explicitly. As a result, it is found that this coupling can generate gravitational wave (GW) amplitude birefringence when GWs propagate over the symmetron backgrounds. Because of the matter density difference, the symmetron profile changes significantly when entering the galaxy, so we need to discuss the extragalactic and galactic situations separately. On the one hand, the cosmological symmetron field follows the adiabatic solution, which induces a parity-violating GW amplitude correction with its exponent proportional to the GW frequency and the traveling distance. On the other hand, the symmetron takes the screening solution within the Milky Way, and the generated GW birefringence is only a function of the GW frequency. By further comparing these two contributions, we find that the extragalactic symmetron field produces the dominant birefringence effects. Finally, with the latest GW data from LIGO-Virgo-Kagra, we place a reasonable constraint on the parity-violating coupling parameter in this symmetron model.