No, they expand or widen out, flat is not a concept because space is not flat. People used to think the Earth was supported by elephants, but we know that by going into space at a distance that the earth is round and hanging on nothing, or supported with gravity, Job 26:7. The higher up you go the bigger the universe looks, just simply go straight up in the air. The distance between solar systems gives the impression of flatness, but as you live in the Milky Way galaxy you know that the planets, moons and stars are not flat in any way. Other Galaxi tic systems are the same. We see billions of stars and clusters of galaxies spread through the universe as we go higher in space.