Gravitational wave conversion into electromagnetic waves in cosmological magnetic field on the Friedman universe background

This paper examines the effect of gravitational wave (GW) conversion into electromagnetic wave (EMW) underthe influence of an external magnetic field. The purpose of the study is to assess the influence of this effect on the amplitude of relict GWs with a frequency of 10-18 - 10-16 Hz. As it is known, the amplitude of thecosmological magnetic field increases when moving backward in time as the inverse square of the scale factor. This means that the conversion effect in the cosmological magnetic field might lead to the damping of relict GWs, explaining the reason for the absence of tensor density perturbation traces in the cosmic microwave background. In this study, a coupled system of differential equations was derived for the propagation of GW and EMW in the Friedman-Lemaitre-Robertson-Walker metric. After that, the system was solved numerically for one of the GW polarizations in during the radiation dominance epoch in the approximation of a uniform magnetic field. The field strength in the present day universe is assumed to be 1 nG - the upper limit on the cosmological magnetic field strength (present day value). As a result, the conclusion was obtained on insignificant influence of the effect of GW conversion into electromagnetic waves in a cosmological magnetic field on the long-wave relict GW amplitude.