Cosmological electromagnetic fields due to gravitational wave perturbations

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Abstract
We consider the dynamics of electromagnetic fields in an almost-Friedmann-Robertson-Walker universe using the covariant and gauge-invariant approach of Ellis and Bruni. Focusing on the situation where deviations from the background model are generated by tensor perturbations only, we demonstrate that the coupling between gravitational waves and a weak magnetic test field can generate electromagnetic waves. We show that this coupling leads to an initial pulse of electromagnetic waves whose width and amplitude are determined by the wavelengths of the magnetic field and gravitational waves. A number of implications for cosmology are discussed; in particular we calculate an upper bound of the magnitude of this effect using limits on the quadrupole anisotropy of the cosmic microwave background.