The problem isn't research; it's that actually building the thing is a multi-trillion dollar expense, unlikely to succeed, and even if it did succeed, it would have major problems:
It does nothing about ocean acidification, so everything in the ocean with hard body parts dies
You need to maintain it for several hundred thousand years. Humans don't have a track record of doing that for things on earth, let alone in space
It leaves us with a reduced pole-to-equator temperature gradient, resulting in significant changes to weather and rainfall patterns