The Great Filter is the idea that, in the development of life from the earliest stages of abiogenesis to reaching the highest levels of development on the Kardashev scale, there is a barrier to development that makes detectable extraterrestrial life exceedingly rare. The Great Filter is one possible resolution of the Fermi paradox.
https://en.wikipedia.org/wiki/Great_Filter
The Fermi paradox is the discrepancy between the lack of conclusive evidence of advanced extraterrestrial life and the apparently high likelihood of its existence. As a 2015 article put it, “If life is so easy, someone from somewhere must have come calling by now.”
https://en.wikipedia.org/wiki/Fermi_paradox
Personally I think it’s photosynthesis. Life itself developed and spread but photosynthesis started an inevitable chain of ever-greater and more-efficient life. I think a random chain of mutations that turns carbon-based proto-life into something that can harvest light energy is wildly unlikely, even after the wildly unlikely event of life beginning in the first place.
I have no data to back that up, just a guess.
Plus isn’t the rate of expansion of the universe increasing? So at some point, even going at light speed, your destination will recede faster than you can travel.
Not really. Galaxies are pretty stable, stars orbit around the central black hole in the galaxy. You can absolutely travel between stars in the same galaxy, even if it takes a thousand years.