What does all of this talk of curvature tell us about the shape of the universe? If space-time is curved around sources of gravitational mass, what does that say for larger scale structure? There is much theory at work here, and as it turns out, our universe could be one of many shapes.

**What is dark matter? Dark Energy?**

I am not going to delve into dark matter/energy more than to give a general definition. Just know that when we measure rotation curves of distant galaxies (plotting the orbital speeds of stars about their galactic center with their distance from it), and compare it to the values we expect (given the mass we see), the two are in disagreement. There is missing mass somewhere that does not emit light. It is believed that this mass has an expansive force on the universe.

The universe began as a singularity (see Black Holes section) prior to the Big Bang, and has been expanding since. In fact, the expansion of the universe is accelerating. How do we know this? The farther out we look into the universe, the higher the degree of frequency shift in the light received. Remember frequency shifting, when an object is moving away from us, the light it emits will have less energy and a lower frequency. What does this tell us about objects in the distant universe? They are accelerating away from us! Lately there have been some interesting findings in measuring the rate of the expansion of the universe.

Above is a picture taken from a great article about very recent (April 2016!) discoveries on the expansion of the universe. The link to the article is here, and is a pretty exciting read!

Tying dark matter into our discussion of the shape of the universe; the density of matter (both dark and emitting) has a lot to say about the fate of our universe, and its current shape. Dark matter seems to slow expansion, whereas dark energy makes it accelerate. Dark matter only interacts with the rest of the universe through gravity, and should have an attractive force on it. But dark energy, a mysterious phenomenon, seems to have the opposite effect in making the universe expand. Given the amount of matter in the universe, expansion should stop, but this is not the case. Welcome to one of the hottest topics in physics right now!

NASA has a wonderful webpage discussing dark matter here.

Remember gravitational lensing? It appears a *dark matter galaxy* has been found using this technique! What a powerful tool! Please follow the link below the image for an exciting read!

One more thing to discuss before we move on is a parameter called** Ω**. In this instance, Ω deals with the critical density of the universe. What is this? It is a ratio: the density of the universe (ρ) divided by the critical density of the universe that is needed to halt expansion (ρ_{critical}).

We will deal with three possible universes in which we live below.

**Universes in three flavors**

In order to discuss the next part, let me begin by saying there is no easy way to refer to three dimension space in these examples. So as usual, we describe things in a lower dimension. Let’s say we have a two dimensional sheet (representing the universe), and based upon the density of matter in this universe, the sheet takes a three dimensional shape. The words “flat, open, and curved” refer to the curvature of space in these universes. Moving on to this below!

**Flat Universe**

A flat universe is one in which the factor Ω takes on a value of 1. A value of 1 means the matter density of the universe is exactly the critical density, so ρ/ρ_{critical}= 1! A flat universe has no curvature in higher dimensions. According to this picture of the universe, expansion should slow down. But from what I mentioned earlier, expansion is actually accelerating! Something is going on that we don’t actually understand, and this is very exciting.

^{(PLEASE SEE “SPACE-TIME CURVATURE IMAGE RESOURCES” FOR VIDEO SOURCE)}

A great video on why the universe is flat!

**Open Universe**

Open universes are ones in which Ω is greater than one. So ρ/ρ_{critical}>1, which means there is more density than critical, so such a universe will expand forever. As we will watch below, an open universe has a net energy that is positive.

**Closed Universe**

A closed universe is one in which Ω has a value less than 1, so ρ/ρ_{critical}<1, which means this universe has density less than the critical density. A closed universe will expand, then eventually collapse back on itself.

**Let’s hear from Neil deGrasse Tyson on the issue!**

^{(PLEASE SEE “SPACE-TIME CURVATURE IMAGE RESOURCES” FOR VIDEO SOURCE)}

As always, Tyson does not cease to take a complex topic and simplify it down. His analogy with negative, neutral, and positive net energies and relating them to orbits is so spot on in it’s simplicity.

**CURVED SPACE-TIME ALSO AFFECTS THE BEHAVIOR OF LIGHT! WANT TO KNOW MORE?**