But we can claim every star that now burns.

No, we can't. As I said, distant galaxies that we can see today are receding, such that no probe we send can ever reach them. Barring aliens already nearby, they will burn unclaimed.

Ouch! I had originally written "every star that burns in the night sky". But that sounded cheesy and pompous even in the context of the comment above. Apparently I failed to replace it with something reasonable before hitting the button.

Perhaps only every star and planet in every galaxy within a sphere centered at earth with a radius of at least a couple of billion light years will be in reach of our technologically mature descendants.

Even as distant civilizations trillions of years hence are lost to each other, forever separated by the expansion of space, their neighbors receding over the cosmological horizon, there can still be rich life in those bubbles. If we survive this eon, life can flourish for the next hundred trillion years.

After that we may be in trouble. After that the cynics may win.