Probing Helical Primordial Magnetic Fields via Chiral Gravitational Waves in the LISA-TAIJI Network

Abstract

Primordial magnetic fields (PMFs) are anticipated to be a cosmological candidate for generating a stochastic gravitational wave background (SGWB) through their anisotropic stress. In particular, if parity violation is present in the production of PMFs, it can induce a helical component in the PMFs, leading to circular polarization in the isotropic SGWB. In this study, we phenomenologically consider parity-violating inflationary magnetogenesis and compute the intensity and circular polarization of the SGWB for several assumed power spectra of helical PMFs. Using the planned sensitivity of the LISA-TAIJI network, we calculate the signal-to-noise ratio (SNR) and perform a Fisher forecast to assess the feasibility of constraining the parameters of helical PMFs. We conclude that it is possible to estimate the helical-to-non-helical power ratio~$r_H$ with ${\mathrm{SNR}}^V>2$ if the PMF strength is $\mathcal{B}\gtrsim 10\mathrm{nG}$ ($50\mathrm{nG}$) in the case of the delta-function-type (scale-invariant-type) PMF spectrum. Our results offer a useful criterion that indicates the future observational limit on helical PMFs at the small scale $k_{\mathrm{LISA}}\approx 10^{12}{\mathrm{Mpc}}^{-1}$.

25 pages, 5 figures