Ask HN: What current startups do you think are changing the world?
[1] http://online.wsj.com/articles/yo-this-app-isnt-so-dumb-1407714995
[1] http://online.wsj.com/articles/yo-this-app-isnt-so-dumb-1407714995
That being said, I see new business opportunities in making sense of exorbitant amounts of data. This can help push further research in areas you have mentioned and obviously many others as well.
Reaction Housing http://www.reactionhousing.com/
Watsi https://watsi.org/
Soylent http://www.soylent.me/
Energy: General Fusion, Helion, and other alternative fusion startups exploring other idea... I feel that the tokamak eats all official R&D funding in this area (and boy can it eat funding). Also a whole gaggle of energy storage startups... grid-scale storage is the missing piece to make renewables really work.
Space: SpaceX, Firefly Space, Blue Origin (debatable whether it's a "startup" or Bezos' pricey side project), Sierra Nevada (not quite a startup but doing new things), etc. (Might even throw in Orbital Sciences, which is a "startup" by average age of aerospace company standards).
Biomedical: Immunity Project, anything in SENS / life extension.
Overlaps quite a bit with old Leary's ideas about priorities...
http://www.futureconscience.com/smi2le-the-futurism-of-timot...
Guy was a bit nuts, but the good kind of crazy.