Fluctuations of the expansion: The Langevin-Raychaudhuri equation

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Scientific paper

We discuss a new semiclassical approach to the investigation of fluctuations of the energy-stress tensor in terms of passive fluctuations of the gravitational field. By using a Langevin version of the Raychaudhuri's equation, one can investigate the effect of stress-tensor fluctuations on the behavior of a bundle of light rays traversing various spacetimes. The gravitational source in each case will be that of a massless scalar field. A useful quantity to accomplish this analysis is the so- called expansion parameter, defined as the divergence of the tangent vector along a congruence of geodesic paths. Calculations of the variance of the expansion reveals the degree to which the image of a distant sources suffers luminosity fluctuations. In principle, this could be used as a check on the viability of certain theories (such as extra compactified dimensions), as well as a prediction of exactly what circumstances might lead to significant effects within the framework of general curved 4D models.

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