Improved limits on anisotropy and inhomogeneity from the cosmic background radiation.

We consider directly the equations by which matter imposes anisotropies on freely propagating background radiation, leading to a new way of using anisotropy measurements to limit the deviations of the Universe from a Friedmann-Robertson-Walker (FRW) geometry. This approach is complementary to the usual Sachs-Wolfe approach: the limits obtained are not as detailed, but they are more model-independent. We also give new results about combined matter-radiation perturbations in an almost-FRW universe, and a new exact solution of the linearised equations. PACS numbers: 98.80.Hw School of Maths, Portsmouth University, PO1 2EG England Computational and Applied Maths Dept, Witwatersrand University, 2050 South Africa Applied Maths Dept, University of Cape Town, 7700 South Africa Vatican Observatory Research Group, University of Arizona, AR85721 USA