How long would it take to travel from earth across the universe and back home to earth again?

uming that space is curved, and that no-thing exists outside of space, and that there is no 'outside' space, then if one travelled in a straight line from this planet in any direction, presumably at some point one should return to earth. So, if one left earth in a starship travelling at the speed of light in a straight line how long would the journey take? And, if at the speed of light time pes slower than on earth, then how much younger would you be than a person of identical age as you, that had stayed on earth?