If you go with the non-animal version of the ending, he represents a world in which doing whatever is necessary for survival is not only okay, it is expected and normal. If the tiger does indeed represent Pi, it symbolizes all of the awful things that he had to do in order to stay alive, including killing someone evil. A tiger is expected to do what is necessary to stay alive; it is expected to kill. But a human being, that's another story; it is morally debatable. So, Richard Parker represents the reality, or existence, that allowed Pi to survive without having to deal with the moral weight of what he had done. What Pi did to survive weighs heavily on his mind, and in order to be able to live every day with that guilt, Richard Parker can take that guilt away from him.
If you go with the animal story of the ending being true, Richard Parker can also symbolize Pi's salvation. Throughout the story, Pi mentions several times that if it wasn't for Richard Parker, he would have given up any hope of surviving. Having another creature to take care of, having company and companionship, that is what keeps Pi striving, working, and alive.
Those are a couple other possibilities for a deeper symbolism behind Richard Parker; I hope that they help! Good luck!