The Density Parameter

In previous posts, I've discussed the density of the universe in terms of all the matter and energy the universe contains. I've also mentioned how the universe has a critical density, i.e. the matter and energy density required to make the universe flat (expanding forever while reaching a finite distance asymptotically.


Let's remember what we mean by open, closed, and flat universes.

• An open universe is a universe that has a smaller density than the critical density. An open universe will expand forever and never reach a finite size.
• A closed universe is a universe with a larger density than the critical density. A closed universe will reach a maximum size then gravity will take over and cause the universe to collapse.
• A flat universe is a universe with a density equal to the critical density.

What we can measure is something called the density parameter, Ω. It is the ratio between the actual density of the universe and the critical density. If Ω is less than one, we live in an open universe. If it is greater than one, our universe is closed. What is the value of Ω?


We know right now that Ω is close to one. We know this from all the observations and measurements we make. The amazing thing is the majority of the mass and energy in the universe can only be inferred by the measurements. Only 4% of the mass and energy is found in stars, gas, and dust that can be directly observed. Dark matter takes up 22% of the mass and energy. And the dark energy is a whopping 74% of the overall density of the universe.


We know that Ω is close to one because of the measurements we make. We also know that the density has to be close to the critical density because if it wasn't, we wouldn't be here.


If Ω was 0.95, the expansion would have been too much for gravity to counteract, gas clouds would not have collapsed, stars and galaxies wouldn't have formed, planets would not have condensed out of the stellar clouds, and life would never have a chance to even exist.


If Ω was 1.05, gravity would have overwhelmed expansion before it even had a chance to start. Without enough time for gas clouds to collapse, again, no stars, galaxies, planet, and yes, life could have formed.


We still don't know if we are in an open, a closed, or a flat universe. Right now, all evidence points to an open universe (with Ω slightly less than 1), but that is what is awesome about science. The search for knowledge means we could learn new things and change our perception of the universe.

What Type of Universe do We Live In?

The last three posts describe the three possible universe types: open, flat, and closed. The question is what will happen to our universe? The real answer is that we really don't know. But we do know this: the universe is very close to being flat if it isn't flat. How do we know this?


The first way is by looking at the cosmic microwave background radiation. We know by looking at the data, we can see that the CMBR is relatively uniform. It could only be that uniform if not only the universe went through inflation, but also if the universe is flat. Any other type of universe would result in a lumpy universe.


Another way we know is by induction. If the density of the universe was just a tad bit smaller than the critical density (say 95% of the critical density), gravity would have lost out to expansion very near the beginning of the universe and would have expanded too rapidly for any galaxies or stars to have formed. Obviously, it must be have more mass and energy than 95% of the critical density because we are here.


Likewise, if the density was 105% of the critical density, then gravity would have overcome the expansion quickly. The universe would have collapsed too rapidly for anything to have formed.


We know then that the universe is relatively flat. The question is, which side of the critical density does the actually density lie? Again, we just don't know. The only thing we know is that we know that the mass density (both dark matter and baryonic matter) that has been measured is about 26% of the critical density but we don't really what the other 74% of the density is. Since we don't know what it is, cosmologists call it dark energy. The dark energy is believed to be a driving force to the expansion of the universe, but what it is made up of is still unknown.

Curvature of the Universe

Last time, we talked about how the universe might end since we really don't know what exactly will happen. There is not enough information for us yet to tell us whether the universe will come collapsing back in on itself or if it will just continue on expanding forever.


What do we know? We do know that the universe is nearly flat. By comparing the overall mass/energy density of the universe to what is called the critical density, we see that the ratio between the two (actual/critical) is very nearly one. As mentioned last time, a ratio less than one will result in an open universe, a ratio of one gives a flat universe, and a ratio greater than one will end up with a closed universe.


Both open and flat universes result in expansion continuing on forever, though a flat universe will asymptotically approach a physical limit for the size of the universe. A close universe will reach a maximum, then as gravity takes over, will begin to pull all matter and energy back towards each other.


Looking at the picture below, we see how the three types of universe relate to each other. The circled area is about where we are now, and you can see how it is difficult to tell if we are in an open universe, a flat universe, or a closed universe.

We can also describe the three different universes in reference to their shapes, which will go into more detail for the three. A flat universe is considered to have zero curvature, hence, it is flat like a piece of paper. Open universes have a negative curvature, like a saddle. Closed universes are said to positive curvature, like the surface of a sphere. Negatively curved space and positively curved space can lead to some strange phenomena which we will learn more about later.