We use holography in order to study the entanglement entropy for a spherical entangling surface in a FRW background with an arbitrary time dependence of the scale factor. The calculation is done in various dimensions, allowing for nonzero spatial curvature. The entanglement entropy of a CFT at nonzero temperature in this background is also considered. Our approach is based on coordinate transformations that relate the extremization problem to the one for a static background, with a careful

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... mination of the UV cutoff. We demonstrate the agreement with the expected form of the entanglement entropy and with various known results in specific cases. In four dimensions, apart from the cutoff-dependent terms, we compute and discuss the finite term related to the expansion rate.