Whether Google is a monopoly in search or not is a determination the anti-trust division of the justice department would have to make, which I don't believe is

Whether Google is a monopoly in search or not is a determination the anti-trust division of the justice department would have to make, which I don't believe is what the current administration is actually suggesting they are going to pursue since they are generally pretty unorganized and that sounds like a lot of work. Anyway even if that were found to be the case (and arguably there's a good case) I don't know if the likely remedy would be to allow the government to control search results. If the government wants to meddle with search results the better approach might be from the FCC which could claim Google needs to operate under some kind of common carrier status I guess.