When the Universe starts to expand from a single point (singularity) and expands to a size of lightyears in just 10 minutes, then it seems to me that there must have been speeds exceeding the speed of light. Surely that cannot happen?!
Einstein's theory of Special Relativity states that information cannot travel from one place to another faster than the speed of light. When the Universe expands, it is the entire of space and time that is expanding. If you imagine two points in the Universe, as the Universe expands, it is the space between them that expands and everything moves away from everything else, so you will not be able to transmit anything (whether radiation or matter) between them faster than the speed of light (in fact the Universe may be expanding so fast that light travelling from one place to the second may not ever be able to catch up with it, so one place will not be visible to the other!)