"The cosmos is all that is or ever was or ever will be. Our feeblest contemplations of the Cosmos stir us—there is a tingling in the spine, a catch in the voice, a faint sensation, as if a distant memory, or falling from a height. We know we are approaching the greatest of mysteries." -Carl Sagan

If you looked out at the planets in the Solar System orbiting our Sun, you'd expect that if you know where they are right now and how quickly they're moving, you can figure out exactly where they're going to be at any time-and-date arbitrarily far into the future. That's the great power that comes with understanding the laws of nature that underlie any physical system: in this case, the laws of gravity that governs the motion of planets in our Solar System.

Image credit: Chaisson, Eric; McMillan, Steve, ASTRONOMY, 2004.

And if the planet you were observing wasn't where it appeared to be, you'd assume that one of two things were amiss.

Either there's extra mass somewhere in the Solar System that's throwing off the motion of the planet you're looking at, due to the effects of its gravity, or Your understanding of the laws of gravity are incomplete, and need to be upgraded or modified in some way.

Believe it or not, this has actually happened twice before in our own discovery of the Solar System.

Image credit: original source Michael Richmond; modifications by me.

For some sixty years after its discovery, Uranus posed a great mystery. Kepler's and Newton's laws were well-known, and yet Uranus (green, above) was observed to move more quickly than its predicted orbital speed, then to move at the predicted speed, and then to move too slowly. The laws of gravity could have been wrong, in principle, but a large, unseen mass (dark blue, above) even farther out could have been affecting its orbit. The discovery of Neptune in the mid-19th Century was the extra mass that was missing from our picture, and explained the anomalies in Uranus' orbit.

Image credit: French Wikipedia user Dhenry.

On the other hand, Mercury's orbit was observed to precess, or to have the elliptical path it traced out rotate in space with respect to Earth. Some of this precession was predicted, both from the difference between a calendar year and an orbital (sidereal) year here on Earth and from the presence of the other known masses in the Solar System. But there was some extra precession beyond what was predicted. There could have been an extra planet interior to the orbit of Mercury; that could have explained it.

But what turned out to be the case was that Newton's law of gravity wasn't the entire story, and needed to be replaced with Einstein's theory of general relativity. It was only when Einstein's theory made additional (non-Newtonian) predictions that were then confirmed, such as the bending of starlight by gravitational mass, that our theory of gravity was upgraded.

Image credit: Hyper-Mathematics - Uzayzaman / Spacetime.

Well, since that time, there have been additional challenges to how gravitation works in our Universe, albeit on much larger scales than our Solar System.

From the 1930s to the 1970s, galaxy clusters and individual galaxies had their speeds measured very precisely for the first time. This meant that the speeds of individual galaxies in clusters could be measured relative to the center-of-mass of the cluster itself, and the rotational speeds of spiral galaxies could be measured relative to the center of the galaxy itself. In both cases, it was found that the motions did not line up with the predictions of general relativity in a Universe where matter was made up primarily of protons, neutrons, and electrons.

Image credit: Rogelio Bernal Andreo of http://blog.deepskycolors.com/about.html.

Again, in principle, there are two reasonable possible resolutions to this conundrum.

Either there is some unseen mass/matter out there, or The laws of gravity need to be modified/enhanced once again.

The leading candidate for the first scenario is the addition of some type of dark matter to the Universe, while the second scenario requires MOND, MOG, the relativistic TeVeS, or some similar type of modification. I've written about these possibilities many, many, many, many times before, but there's one very simple test that you can apply to tell which of these two possibilities are consistent with our actual Universe. A test that -- spoiler -- the advocates of #2 are terrified of bringing up in their own papers.

Image credit: Mark Subbarao, Dinoj Surendran, and Randy Landsberg for the SDSS team.

You look at the Universe on the largest scales. Not on the scale of stars, nor at individual galaxies, not even at clusters or supercluster of galaxies, but at the entirety of the visible Universe. Those scales, the largest possible scales.

Because on those scales, there's no denying that gravitational forces dominate, and the other forces are all but insignificant. If you can accurately measure how the Universe clusters on the largest scales, you can compare the predictions of a general relativity + dark matter-dominated Universe with what you observe, as well as a no-dark-matter + modified gravity Universe, and see what you get. Below is the prediction of the standard ΛCDM cosmological model (GR + dark matter).

Image credit: Michael Kuhlen, Mark Vogelsberger, and Raul Angulo.

In particular, it's the largest scales -- all the way on the left -- that are the best and most robust test of these two scenarios. While many other variables enter into play (and the uncertainty rises) the farther to the right you're willing to go, the largest scales are the simplest and most straightforward test of which of these possibilities is correct. Why's that?

On these scales, simulations are not required, and the way the largest-scale structures in the entire Universe are distributed/correlated (which is what the Power Spectrum measures) is known, exactly. So what do we see when we look out at the Universe on these largest scales, and compare with the predictions of these different scenarios?

Courtesy of Scott Dodelson, I present to you the one graph that incontrovertibly settles the matter, at least for the time being.

Image credit: Scott Dodelson, from http://arxiv.org/abs/1112.1320.

Those red points (with error bars, as shown) are the observations -- the data -- from our own Universe. (Courtesy of the Sloan Digital Sky Survey.) The black line is the prediction of our standard ΛCDM cosmology, with normal matter, dark matter (in six times the amount of normal matter), dark energy, and general relativity as the law governing it. Note the small wiggles in it and how well -- how amazingly well -- the predictions match up to the data.

Now look at the blue curves: these are models with no dark matter. The dotted blue curve is what you'd get in a no-dark-matter Universe that abided by general relativity. The "wiggles" you get are far too large in amplitude, and the spectrum fails to rise on progressively smaller scales as required by our Universe. The solid blue curve is what TeVeS -- the relativistic version of MOND -- predicts. It can raise the overall amplitude of the Universe's power to an appropriate level at a few select points, but the spectrum is all wrong. Ruinously wrong. It's not even close to viable.

And until those in favor of modifying gravity can successfully predict the large-scale structure of the Universe the way that a Universe full of dark matter does, it's not worth paying any mind to as a serious competitor. You cannot ignore physical cosmology in your attempts to decipher the cosmos, and the predictions of large-scale structure are some of the most basic and important predictions that come out of physical cosmology. And that's why the Universe needs dark matter -- and not MOND, MOG, TeVeS, or any other dark-matter-free alternative -- in one all-important graph!