The Simplest Argument For Dark Matter

> “What makes the universe so hard to comprehend is that there’s nothing to compare it with.” -Anonymous

If I were brand new to theoretical cosmology, I might be skeptical of a whole bunch of “dark” things that I’d heard of. “Dark matter?” “Dark energy?” Come on; you’ve got to be kidding me! You’re telling me that 95% of the Universe is not made of protons, neutrons, and electrons, like all the matter we know?

After all, I look out at the Universe, and this is what I see.

Stars, galaxies, gas and dust… normal matter, all of it. Yet all I need to do is start with two very well-supported assumptions, and you can demonstrate to yourself that the matter in the Universe must be mostly, but not completely, made up of dark matter.

The first assumption is that the Universe follows Einstein’s General Relativity as its law of gravity.

The second assumption is that the Big Bang picture of the Universe works.

(And yes, you astute ones, it is unfair to place the Big Bang before inflation, as this graphic does.)

You give me these two things, and I can, unambiguously, give you dark matter.

How’s that?

Because that’s what the laws of physics let us do!

We start with a hot, dense, nearly (but not perfectly) uniform Universe that’s expanding, and it unequivocally follows (among others) the following steps:

1. It expands and cools down, 2. It forms the light elements through nucleosynthesis, 3. Matter starts to collapse under its own gravity, while radiation (like photons) push back against it, 4. Neutral atoms form, leaving a snapshot of the Universe at that time (the CMB), and 5. Gravity pulls the neutral matter together into stars and planets on small scales, and globular clusters, galaxies, galaxy clusters and superclusters on large scales.

The big distinction, of course, is that radiation doesn’t push back against dark matter, but does against normal matter (i.e., protons, neutrons, and electrons).

So what does this mean for what’s in our Universe?

It means that when we look out at the temperature fluctuations in the Cosmic Microwave Background (above), we can figure out whether our Universe is full of normal matter, dark matter, or both, and how much of each of them. In fact, there’s an online calculator here that lets you put in your own parameters for how much normal matter, dark matter, and dark energy you want, and gives you the spectrum of CMB fluctuations. (Try it if you like!) Here are the observations that you need to match:

And can you do it with practically no normal matter?

Nope. But try it with all normal matter (and no dark matter), and guess what?

You can’t do it either! If you want to make it work:

You need a mix of about 20-25% dark matter, about 4-5% normal matter, and let the rest (for a total of 100%) be dark energy.

But that’s not the only large-scale piece of evidence we can test like this. There’s also the large-scale-structure we find in the Universe!

(Image credit: 2dF galaxy redshift survey.)

And what we can do with this map is ask, if I look a certain distance away from a galaxy, how likely am I to find another galaxy? The result is known as the Matter Power Spectrum of the Universe, and it looks something like this.

Here’s the thing: if the Universe were only full of normal matter (and not dark matter), the spectrum wouldn’t look smooth like this! It would have certain regions where the spectrum dropped out to zero, corresponding to scales where normal matter were “pushed away” by the radiation in the early Universe.

But dark matter doesn’t get pushed by radiation, and so if the Power Spectrum doesn’t have these features, the Universe must have more dark matter than normal matter!

But — and here’s the most convincing part — if you design your Universe with about 70-75% dark energy, 20-25% dark matter, and about 4-5% normal matter, you get predictions that match up perfectly with our observations!

And remember, all I needed to do this? General Relativity + the Big Bang. And the rest I figured out from the physics: by computing my predictions and comparing them with the data. And that’s how we know there’s dark matter! You want a Universe without dark matter, and — at the very least — you have to throw out General Relativity.

And trust me, you don’t want to make Einstein angry… Read the comments on this post…


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