The Right to Privacy is not changed simply because you are a renter. You have the very same constitutional rights as anyone else. Do remember that the constitution only protects you against the government and government agents. It does not over ride your rental agreement if that allows or requires inspections on the part of the landlord.
In certain states (IL is where I am and this is true here) the landlord must give AT LEAST 24 hours notice before entering a rented establishment unless there is an emergency (a fire for example) in which case they can enter unannounced although the idea is that it would be an emergency...