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.

Cosmological Constant

When Albert Einstein applied his equations of General Relativity to the observable universe, he found something that he didn't like. His equations were correct, but for some reason, his equations predicted that the universe was dynamic when he and everyone else though the universe was static. This was in 1917, before the Big Bang theory and before Edwin Hubble found that the universe was expanding. To account for what he felt was incorrect, he introduced a fudge factor to take away the dynamic universe solution. He called his fudge factor, the cosmological constant. He hoped and felt that in time, physics and astronomy would be able to allow the cosmological constant to go away. When Hubble found the expansion of the universe and the Big Bang theory were proposed, Einstein thought that his cosmological constant was his biggest blunder. But was it?


Now, with the introduction of dark energy to help explain the expansion of the universe, the cosmological constant was reintroduced. As explained last time, if the dark energy density is constant, the universe will be open and expand forever. With a constant dark energy density, this implies that the universe is homogeneous in both space and time. Remember that this is referred to the Perfect Cosmological Principle which was briefly mentioned here. In other words, the universe appears static and therefore, the cosmological constant may be a physical quantity describing the dark energy density of the universe. Unfortunately, we still don't know what the dark energy density is doing and it may be centuries or millennia before we know.

Dark Energy

What is dark energy?


First, what isn't dark energy? It isn't energy used by either Sauron or Lord Voldemort. They use dark magic, which isn't the same. You also shouldn't confuse it with negative energy, which is strange phenomena in itself. We will look at negative energy later.

Dark energy is defined as the energy that permeates space and drives the expansion of the universe. At the present time, the amount of dark energy in the universe is seeming to accelerate the expansion rate of the universe. It should be noted, however, that this does not mean that the universe is open. Just because the universe's rate of expansion is accelerating now, it does not mean that sometime in the future, the rate of expansion can slow, stop, or reverse.


Dark energy is thought to be one of two things: a constant energy density over time and space (static) or a scalar field density that has a value that can change with time or space (dynamic).


If the energy density is constant over time and space, that means as the universe expands, the amount of energy (not including mass) must increase. The only way this happens without violating the conservation of energy is that mass must be converted to energy in some way. This could be done in the normal way (matter-antimatter collisions) or in some way that we don't know. This constant energy density is referred to as the Cosmological Constant, and was first introduced by Albert Einstein. We will discuss this more later. If this is what dark energy is, then we live in an open universe.


The other is that dark energy density is a changing quantity which in the future could either slow down (but not stop - open universe), stop (flat universe), or reverse (closed universe) the expansion, depending on how the density changes over time.


At our current knowledge, dark energy is 68.3% of the total mass-energy density, dark matter is 26.8%, and ordinary matter is only 4.5%. So you can see, what we don't know about the universe is a heck of a lot more than what we do know.

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.

A Closed Universe

The last type of universe that we could possibly live in is called a closed universe. The best way to describe a closed universe is one that does not comes back in on itself, or in other words, it closes in on itself. The best example of a closed 2-D space is the surface of a sphere. Unlike, a 2-D flat space or a 2-D open space, a closed 2-D space does not have an edge. When it expands, it expands equally in all directions, uniformly. The spaces are said to be positively curved, because they do not expand in opposite directions.

Looking at the sphere, you can see that as it expands, all points on the surface expand uniformly from the center, and are equidistant from the center at all times. A 3-D closed universe (positively-curved space) would be similar, but in higher dimensions. Another unique thing about a closed universe, is that no matter where you started on a path, eventually, you'd end up at your starting point even without turning, though it may take an infinitely long time. In both open and flat universes, you could never reach your starting point without turning.

Closed universes are also different in lines that start out parallel, end up converging at large distances. Take lines of longitude on the Earth. They start out parallel at the equator, but as they approach either pole, the converge. Because of this, the sum of the interior angles of a triangle are always greater than 180°.

How would we know if the universe is closed? In this case, the actual density of the universe will have to be larger than the critical density. This means that eventually gravity in the universe will slow down and stop expansion at some maximum size. Gravity will then take over and start attracting all the matter and energy together again. When the matter and energy reach the singularity, the Universe will end in a Big Crunch. It is believed that if this is the way the Universe ends, it may be the beginning of a new universe with another Big Bang. This type of universe is called an oscillating universe.