The big rip
If dark energy grows (per cm³) with the size of our universe then we will eventually reach a singularity where the size of our universe go to infinity in finite time. The force pulling everything apart would become stronger and stronger.
0. Galaxy clusters would disintegrate
1. Galaxies would fall apart
2. Planets would be be pushed away from their stars and each other.
3. Your planet itself would fall apart.
4. Molecules and atoms would be torn apart or unknown physics would come into play.
https://arxiv.org/abs/astro-ph/0302506
https://www.youtube.com/watch?v=kCofnejCZGU
https://www.youtube.com/watch?v=t00pfJnEt48
So survive a little longer you would need a capsule or a space-suit that traps air for you to breath, of course eventually the force would be so strong your capsule/suit would be pulled apart but by then you might already be dead since the force acts on your body itself. Your body would be torn into pieces and these pieces would later be torn into even smaller pieces, this would continue until atoms themselves are destroyed, nothing would survive. It's unclear what if anything would follow.
Evidence in favor of the big rip
Current measurements strongly indicate that dark energy is getting stronger which does support the big rip theory.
https://arxiv.org/pdf/2103.01183.pdf
https://arxiv.org/abs/1907.10625
https://arxiv.org/abs/2003.07355
https://arxiv.org/pdf/1910.02978.pdf
https://www.youtube.com/watch?v=uoAkFq-KIrk
https://www.youtube.com/watch?v=t9N9S4loyu8
Resolving the Boltzmann brain issue
If our universe would just keep expanding forever you would be infinite times more likely to be a Boltzmann brain.
https://arxiv.org/pdf/0802.0233
This is resolved by having our universe be destroyed completely or having it be cyclic.
Big rip cyclic cosmology
One possibility is that the big rip will give birth to a new universe that may have different physics than our current universe, our current understanding of physics isn't good enough to know what would actually happen.
https://arxiv.org/abs/2005.12684
https://arxiv.org/abs/1911.06456
This could resolve the apparent fine-tuning problem.
researchgate.net/profile/Kevin_Ludwick/publication/236215355_Cyclic_Cosmology_from_the_Little_Rip/links/57d94c4408ae0c0081efab58/Cyclic-Cosmology-from-the-Little-Rip.pdf
https://medium.com/starts-with-a-ba...big-rip-lead-to-another-big-bang-566a4fbb0f25
Of course it's unclear how much stronger the phantom energy would get before unknown physics come into play that alter the trajectory, it might not actually be a "big rip" in the strictest definition (space-time itself being torn apart).
https://arxiv.org/pdf/2006.15060.pdf
How to properly disprove/falsify the big rip 'theory'
We would need to find a more fundamental theory that is clearly the correct one and from that we will see what will actually happen. I have looked at various attempts at a more fundamental theory of physics but none of these look particularly promising to me so i do not think we have much to go on here.
