So really the question becomes "whose authority," and who recognizes that authority.
In the days when tribe and chuch could force men and women to take care of their children, that authority was sufficient. Now it takes the power of a state to do so.
Societies have a never ending need for replenishment. New generations must arise and believe what that society believed, or it will cease to exist. Marriage is the construct that makes any civilization possible. 'On who's authority' is a valid question, but without any authority, there would be no marriage.