Motomu Toriyama, producer of Lightning Returns: Final Fantasy XIII has told VG24/7 that the game will not have multiple endings, and will give fans a definitive ending to the series.
"The concept behind the design of Lighting Returns is that it will be the concluding chapter of the Lightning Saga. Unlike in the previous title, there will not be multiple possible endings created from differently branching interpretations of history, but instead the story will lead to the one true ending." Said Toriyama. He goes on to say "Having said that, the game is structured so that time is constantly ticking away during gameplay and the world moving and changing with it, meaning that every time you play through you can have a new experience."
One of the core concepts in Lightning Returns is that the game will move in some form of real time, so you will have to complete the game more than once to experience everything that occurs in the world.