Circularly polarized scalar induced gravitational waves from the Chern-Simons modified gravity

We investigate the scalar induced gravitational waves (SIGWs) in the Chern-Simons (CS) modified gravity during the radiation dominated era. The SIGWs are circularly polarized, which provide us a tool to test the possible parity violation in the early universe. We derive the semianalytic expressions to evaluate the fractional energy density of the SIGWs, $\Omega_{\mathrm{GW}}$, which receives contributions from the general relativity (GR) and the correction due to the parity-violating term, respectively. We find that the degree of the circular polarization of the SIGWs can be as large as of order unity, although the contribution to $\Omega_{\mathrm{GW}}$ from the CS term is at most of the same order as that from the GR.