The graviton is the name given to the particle that would carry the force of gravity. It has never been detected, but is required if gravity is to be understood in the same way as the other fundamental forces. This way of thinking about the nature of gravity is different from the geometrical description in Einstein's general relativity. However, one could take it to mean a non-Euclidean geometry for space. They are trying to get around the limitation of the speed of light for traveling through the universe.
Light is energy, and in general relativity energy is affected by gravity just as is mass.
Time travel isn't possible in special relativity. But how about General relativity. What we are looking for when we are trying to do time travel, is a timelike worldline through space-time that moves into the future of some event A and ends up in the past of event A without ever exceeding the speed of light. Remarkably, there are solutions of Einstein's equations that contain such curves. Another is the so-called Goedel solution for a rotating universe.