New Primordial-Magnetic-Field Limit from The Latest LIGO S5 data

Since the energy momentum tensor of a magnetic field always contains a spin-2 component in its anisotropic stress, stochastic primordial magnetic field (PMF) in the early universe must generate stochastic gravitational wave (GW) background. This process will greatly affect the relic gravitational wave (RGW), which is one of major scientific goals of the laser interferometer GW detections. Recently, the fifth science (S5) run of laser interferometer gravitational-wave observatory (LIGO) gave a latest upper limit ${\mathrm{\Omega }}_{GW}<6.9\times {10}^{-6}$ on the RGW background. Utilizing this upper limit, we derive new PMF Limits: for a scale of galactic cluster $\lambda =1$ Mpc, the amplitude of PMF, that produced by the electroweak phase transition (EPT), has to be weaker than $B_{\lambda }\le 4\times {10}^{-7}$ Gauss; for a scale of supercluster $\lambda =100$ Mpc, the amplitude of PMF has to be weaker than $B_{\lambda }\le 9\times {10}^{-11}$ Gauss. In this manner, GW observation has potential to make interesting contributions to the study of primordial magnetic field.