Do private investigators have the right to actually break in to people's houses or 'arrest' them?

Most private investigators work for Bail Bond company's. They will have a warrant to arrest bale jumpers. It's a dangerous job. The warrant is issued by the court for the persons arrest. So they do have legal authority to make arrest. If you catch a person doing a crime, you can place them under citizens arrest, call the cops and file complaint. Most people wont do this due to the danger involved.