Probing parity violation in the stochastic gravitational wave background with astrometry

Astrometry holds the potential for testing fundamental physics through the effects of the stochastic gravitational wave background (SGWB) in the $\sim 1–100\mathrm{nHz}$ frequency band on precision measurements of stellar positions. Such measurements are complementary to tests made possible by the detection of the SGWB using pulsar timing arrays. Here, the feasibility of using astrometry for the identification of parity-violating signals within the SGWB is investigated. This is achieved by defining and quantifying a nonvanishing $EB$ correlation function within astrometric correlation functions and investigating how one might estimate the detectability of such signals.

Figure 1

Top: the functions $\alpha (\mathrm{\Theta }){\sin }^4\mathrm{\Theta }$ and $\beta (\mathrm{\Theta }){\sin }^4\mathrm{\Theta }$ defined in Eq. (13); bottom: $F_{+\times (\times +)}(\mathrm{\Theta })$ and $F^V(\mathrm{\Theta })$ defined in Eq. (18).

Figure 2

The log-log plot of the angular power spectrum Eq. (24) for the first thirty multipoles. The red dots are the coefficients obtained from $F_{\times +}$, and only contribute to the even modes. The blue dots are those from $F_{+\times }$ and only contribute to the odd modes. One can see that the angular power spectrum falls roughly as $l^{-5.8}$. We provide the exact numbers in Table 1 below.