And even at the speed of light, we would never reach "The end of the cosmos," because the universe is expanding at the speed of light.

Hense why as you go closer to the speed of light you experience time more slowly than an observer, because time is basically a by-product of this expansion. You would never even reach the next galaxy because we're moving away from each other at the speed of light.

Edit: At least not with this method. We would need a warp like in Event Horizon.