The cosmological expansion of space causes distant pairs of points to become receding from each other at a speed greater than the speed of light, so it is impossible to communicate or travel between them… unless you have a warp drive. (Is such travel forbidden by general relativity? I'm guessing not: "just" connect a wormhole between the two points.)
Tell a story of if you did have such a device to travel beyond the edge of the observable (from your starting point) universe, beyond the cosmological horizon. It sort of puts science fiction like Star Trek and Stargate SG-1 to shame, as they merely use their warp technology to travel around just one galaxy within the time frame of human lives. How about going somewhere actually impossible to reach, or even see, distances so great that it makes galaxies look like dust?
The traveler will encounter "more of the same" because the physical laws of the universe aren't going to change at the cosmological horizon. This suggests a challenge: explore Tegmark's Level 1 multiverse. Find other places in the universe similar or identical to here. This might require another technology: sensors which can observe vast regions of space, most of it way beyond the cosmological horizon, and a vastness on the order of googolplexes of Hubble volumes, but all still reachable by warp drive.
I imagine such a sensor would consist of some warp-speed variant of a gravitational wave, organized into a tree structure to quickly answer a search query scanning the entire multiverse.
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