Just to emphasize what lisper is saying, the core problem is exponential growth, even if we invent FTL spaceships, even if we invent warp drive, the core problem is still exponential growth.

We could turn the Galaxy green† and still not have enough room. We could fill it with Ringworlds, with Dyson Spheres, and still not have enough room.

The core problem is exponential growth.

† https://en.wikipedia.org/wiki/The_Millennial_Project:_Coloni...