To protect your rights most times a police officer or police have to have a search warrant from the court to enter your house without your permission.
But there are some circumstances that allow a cop to enter a home without a warrant such as if someone has escaped prison or has robbed some place and that person got into your house and is hiding then the police may enter your home to apprehend the suspect to protect themselves and the community.
Another reason cops can enter your home without a warrant is if they get a call saying someone has been stabbed or shot inside your home then they can search your home without a warrant.
Other times the police need a warrant to enter your home but for probable cause they don't need a search or enter warrant.