Well, @Symbeline beat me to discussion of my number one staggering point, infinite time-space. As he says, it boggles the human mind, yet claiming it doesn’t exist is equally unsatisfying. Space ends in a wall? What’s beyond the wall. Time starts at the big bang? Yet to an observer outside our space time, it didn’t. In their view, there was the time before the big bang. How much time? Again, is there a wall?
But since that one is taken, dark matter is another great conundrum. One of those things that almost must exist but violates much we know if it does. We can’t see it or measure it, but we need it to make some of our theories work. However, having it makes others fail.
I’ve discussed this elsewhere, so I will copy: The mass of the Universe is designated as Omega (Ω). By definition, an Omega of 1 would be the exact amount of mass needed for the Universe to expand to a certain point, then hang at that boundary, neither expanding nor collapsing back into itself due to gravitational pull. For all Ω below 1, the Universe will expand forever. For all Ω greater than 1, it will collapse back into a Big Crunch.
We like to think that Ω should be 1. We can measure observable matter and infer what the Universe’s mass must be, but we find it is about 0.25. Our current answer to this “missing mass” problem is that there must be “cold dark matter” and “hot dark matter” accounting for nearly 75% of the mass of the universe. Not so tidy. We have never observed this to exist any more than we have seen God under a microscope. As of now, the only justification for the existence of dark matter is that it makes our calculations work. So are we really calculating Nature’s laws, or coming up with formulas to match our own imperfect observations?
Further, the CORE satellite has observed a lack of uniformity in background radiation left over after the theorized Big Bang. This is exciting because the observations match pretty closely with what our theories predict for a universe with Ω = 1. Very cool—except that if the universe has a mass of Ω = 1 then the outer arms of spiral galaxies rotate at the wrong speed., They actually revolve around the galactic nucleus at more like what we would expect for our observed Ω of 0.25.
So does dark matter exist? If so, is it so stealthy that it only exists for the theories that need it to balance their equations? Or do we need better theories?