Claudius's assumptions

I believe that Claudius may think that Hamlet is faking or at least knows something. First of all as soon as the play ends he tells Rosecranz and Guildenstern to take Hamlet to England as soon as possible at the begining of act 3.3. Another issue that points to Claudius's awareness is that he is so concerned with why Hamlet is mad. He sends for Hamlet's friends to spy on him, he agrees to test Polonius's theory and continue to use him just to figure out why his nephew/ son is acting insane all through Act 2.2. He does all this when as Gertrude has a perfectly reasonable explanation, that his father had just died and she re-married rather fast. I guess I think that Claudius just acts as if he has somthing to worry about where Hamlet's madness is concerned. I think that Claudius thinks that if Hamlet knows what he did he could either have gone insane or that he would do whatever it takes to get revenge. Claudius is smart, he managed to kill his brother and marry his wife and Hamlet has made a few connections from conversations his Uncle has had in his own insane speeches, if Claudius ever picked up on any of those, he could think that Hamlet is faking.