Light Fluctuations Due to an Intergalactic Flux of Gravitational Waves

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Abstract
A formula is derived that gives the time dependence of the intensity of a light beam that has passed through an arbitrarily varying gravitational field. The formula is valid to second order in the gravitational field strength and is valid only in the geometrical-optical limit for the light beam. An application of the formula to the case where there is only a single source of gravitational field, such as a binary star system, shows that the effect is exceedingly small. Then the case where space is filled uniformly with gravitational radiation is considered. It is found that for a small light source at a distance of a few billion light years the largest effect that can be expected amounts to an intensity variation of a thousandth of a percent. At larger distances it is conceivable that there would be observable intensity fluctuations; however, the formulas derived in this paper are not valid at such great distances.