Imprints of gravitational-wave polarizations on projected tidal tensor in three dimensions

Abstract

Gravitational waves (GWs) distort galaxy shapes through the tidal effect, offering a novel avenue to probe the nature of gravity. In this paper, we investigate how extra GW polarizations beyond those predicted by general relativity imprint observable signatures on galaxy shapes. Since galaxy shapes are measured as two-dimensional images projected onto the celestial sphere, we present three-dimensional statistical quantities of the projected tidal tensor sourced by the tensor perturbation. We show that the presence of extra polarization modes modifies both the amplitude and angular dependence of the correlation functions. Furthermore, we identify a distinct observational channel for probing parity violation in helicity-two and helicity-one modes. In particular, we show that if they propagate at different speeds, galaxy surveys can disentangle the source of parity violation. Our findings establish a theoretical framework for using upcoming large-scale galaxy surveys to test modified gravity theories through the polarization content of GWs.

Figures (8)

• Figure 1: The auto-correlation of the projected traceless tensor field with $c_\lambda=1$. The gray dashed line corresponds to the case where only the longitudinal component is present, which can be regarded as a fiducial line. Other lines are depicted by assuming that $10\%$ of the total power is distributed to other modes.
• Figure 2: The cross-correlation of the vector and curl vector assuming that the helicity-two and helicity-one modes are maximally chiral, that is $P^{(-2)}=P^{(-1)}=0$. We also assume that the speed of the helicity-one wave equals to the speed of light. The black dashed line is depicted without the vector mode.
• Figure 3: The cross-correlation of the vector and curl vector without assuming the maximally chirality for helicity-one waves. We assume that the speed of the helicity-one waves equals to the speed of light.
• Figure 4: Dependence of the speed of the helicity-one wave on the cross-correlation of the vector and curl vector assuming a maximal chirality for the helicity-two and helicity-one modes. The distribution of the power is fixed to be $N^{(+2)}=N^{(+1)}=0.5$, which corresponds to the green line in figure \ref{['Fig. PlotcVVT']}.
• Figure 5: The auto-correlation of the curl scalar assuming that the helicity-two and helicity-one modes propagate with the speed of light. The black dashed line is drawn by neglecting the vector mode.