Faster than light

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I understand that in our universe, the speed of light represents a limit which objects of mass cannot reach. I also understand that at sufficiently high energies, the electromagnetic force becomes unified with the weak force to make he electro-weak force. Now my question is, is energy transmitted faster then light through an electro-weak field? what about a strong field? Etc. etc. It seems to me that energy would be transmitted faster through these fields, and that if it didn't, particles would not be able to exist (my extended interpretation of Fermat's theorem). If this were the case, I would presume there would be serious implications regarding the time-evolution of the universe from the Big-Bang.