LAUSR

Primordial magnetic fields (PMFs) can source gravitational wave background (GWB). In this paper, we investigate the possible constraints on small-scale PMF considering the ongoing and forthcoming direct detection observations of GWB. In contrast to the conventional cosmological probes, e.g., cosmic microwave background anisotropies, which are useful to investigate large-scale PMFs ($>1 {\rm Mpc}$), the direct detection experiments of GWB can explore small-scale PMFs whose scales correspond to the observed frequencies of GWB. We show that future ground-based or space-based interferometric gravitational wave detectors give a strong constraint of about $10^{2} {\rm nG}$ on much smaller scales of about $k\approx 10^{12} {\rm Mpc}^{-1}$. We also demonstrate that pulsar timing arrays have a potential to strongly constrain PMFs. The current limits on GWB from pulsar timing arrays can put the tight constraint on the amplitude of the PMFs of about $30 {\rm nG}$ whose coherent length is of about $k\approx 10^{6} {\rm Mpc}^{-1}$. The future experiments for the direct detection of GWB by the Square Kilometre Array could give much tighter constraints on the amplitude of PMFs about $5 {\rm nG}$ on $k\approx 10^{6} {\rm Mpc}^{-1}$, on which scales, it is difficult to reach by using the cosmological observations.