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How can we compare dark matter and dark energy?

If the units of dark matter and dark energy are different (which I guess they are) then how can the numerical quantities of each be compared with each other? I know that dark energy is sometimes referred to as a "force," but energy does not have the dimensions of a force or a mass. How is it possible to compare "things" percentage-wise if they don't have the same physical units?

When we compare dark matter to dark energy, we aren't really comparing the matter and energy directly; what we're really comparing is the strength of the dark matter's gravitational attraction with the strength of the dark energy's repulsion. So when you hear about the universe being 73 percent dark energy and 27 percent matter (most of the matter is dark matter, but not all of it), then roughly speaking, you can think of these numbers as the relative effect of each component (the matter pulling in, and the dark energy pushing out) on the universe's expansion.

Probably the most intuitive way to think about it is in terms of forces. Suppose you have two galaxies separated by a large distance in the universe, and you want to know what is the force between them that is either pushing them apart or pulling them together. For technical reasons (based on how the above percentages are defined), if you want to specifically compare the forces, you have to divide the number for the matter by 2 before comparing them. So you take 73 percent for the dark energy, and 27 percent divided by 2 (i.e. 13.5 percent) for the matter, and compare them; their ratio is around 5.4.

What this means is that for any two faraway galaxies in the universe today, the force of dark energy pushing them apart is 5.4 times stronger than the force of all the universe's gravity pulling them together; therefore, the end result is a force pushing them apart, which is why the universe's expansion is accelerating. (Keep in mind the important caveat that this only applies for galaxies which are far away from each other; if the galaxies are too close, then the effects of local gravity can become important and overwhelm the cosmological effects.)

January 2005, Dave Rothstein (more by Dave Rothstein) (Like this Answer)

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