Hi. The question above arises out of things like "The universe is 13 trillion years old." The assumption seems to be that everyone experiences time at the same rate, even though we know this isn't true. Relativity posits that as anyone accelerates, time slows down. GPS satellites have to take this skew into account to even work. So why does this get ignored in cosmological models?
Consider the following thought experiment. I get in a spaceship that can accelerate to any speed less than c. It stands to reason that such a craft could go fast enough that its clock would only move 1 year in the time that the vessel went from here to the nearest star. Yet, as it looks back at earth, it would see 4, possibly 5 orbits completed (depending on the exact fraction of c necessary to cause this degree of time dilation).
When we look at other galaxies the stars are moving too quickly to stay gravitationally bound to the system. Is Dark matter (or a portion of it) simply an optical illusion born out of time flowing in that galaxy at a different rate than ours? Can the observed motion in galaxies be slowed down enough to become gravitationally bound without using dark matter? If so, is this impossibly slow? Will it be the same for each galaxy (I predict no, see below).
Two points define a dimension, a ray. Our present time and the "big bang" are 13 trillion years apart. Consider now an observer on a planet flung by a black hole to .9c some 10 trillion years ago. If that observer measures how old the universe is would they come up with the same answer? No.
Also, speed is a "change of position over time." c is ~300,000 km/s. Whose second though? Ours? The observer on the space ship that will perceive itself to reach Proxima Centari in a year even though far more pass on earth? The observer flung to .9c as observed from earth? How do we know we aren't the ones going .9c relative to another observer?
Other galaxies are on different points of this literal timeline. For that statement to be false there would have to be a privileged reference frame, and that's already been proven not to exist through GPS satellites and other experiences. Everything on the line is moving away from the origin - the big bang.
Are the stars of the Milky Way moving too fast to be bound to the gravitational center? I ask this because, presumably, the stars in our galaxy should be in close to the same relative time frames - but not exactly. Stars near the center are moving faster through space, and therefore slower through time. Matter close to black holes should be moving the slowest of all through time.
In summary, I have grappled with these questions in my head a long time, but keep arriving at the conclusion that at least some of the problems observed with dark matter, possibly dark energy, come from shoehorning our own reference frame of time when we should know better given what we know of relativity.
Or, more likely than not I'm missing something.