Description
Primordial magnetic fields (PMFs) are anticipated to be a cosmological candidate that generates a stochastic gravitational wave background (SGWB) by their anisotropic stress. In particular, if parity violation is present in the production of PMFs, it can induce their helical component, leading to circular polarization in the isotropic SGWB. In this study, we consider parity-violating inflationary magnetogenesis phenomenologically and compute the intensity and circular polarization of SGWB for various assumed power spectra of helical PMFs. By using the planned sensitivity of the LISA-TAIJI network, we calculate the signal-to-noise ratio (SNR) and also perform a Fisher forecast to discuss the possibility of constraining the parameters of helical PMFs. We conclude that it is possible to estimate the fractional helicity~$r_\mathrm{H}$ with $\mathrm{SNR}^{V}>2$ if the PMF strength is $\mathcal{B}\gtrsim 10~\mathrm{nG}$, particularly in the case of the delta function type Pspectrum. Our results offer a useful criterion that indicates the future observational limit on helical PMFs on the small scale $k_\mathrm{LISA} \approx 10^{12}~\mathrm{Mpc}^{-1}$.
