can a cop come in your house without a warrant and without being invited in?
Under some circumstances, yes. For example, the police can enter without a warrant if they have good reason to believe that someone inside is in danger, or that something inside the house (a gas leak, for example, or a bomb) presents a danger to those nearby. They can also enter if they are in hot pursuit of a fleeing felon whom they have good reason to believe has entered the house. There may be other situations which would also justify a warrantless entry.