How did cosmology change during the Renaissance?
Well, it changed their perspectives about the things they believed about cosmology before.
First is the position of the Earth, before, they believed that the Earth is at the center of the universe. But Copernicus developed a theory that the Sun is at the center of the Solar System and the Earth just revolved around it. This is also known as the Heliocentric view of Copernicus.
This theory is proved by Galileo who invented the telescope, and saw that the Earth is indeed revolving around the sun, not the other way around. But these were not accepted before, because the church believed that the Earth is at the center of the universe.
Second is they found out about the moon and its dark and light side And other things about the universe is soon discovered because of the invention of the telescope. They can study stars, the sun, and other things on the space.