You are free to live with whoever and wherever you want.single married or divorced.Living with another partner after divorce may affect any settlement.
Spousal maintenance could be affected by you cohabiting, though.
Otherwise, a person can live with whosoever they please. Think how many married people have left their spouse and immediately moved in with their lover.
This may have its basis in Sharia Law. I seem to remember that in Islam a divorced woman cannot remarry for a specified time to ensure that she is not pregnant and doubt could be cast over paternity.