###### By Don Lincoln**, **Fermilab

## The hard part of cosmology is determining through experimental data such parameters as the size of the universe, its age, how it is expanding now and how it did in the past. There are several measurements, each of which use separate data. How?

### A Flat Universe?

The radius of the visible universe is currently 46 billion light-years and it reflects the absolute farthest that it would possibly be able to see. But that’s just the visible universe. There’s no reason to think that the universe just stops there. If, somehow, we had some sort of magic spacecraft and could go 46 billion light-years away, that space would look much like it does here. So, space extends beyond farther than we can see. But then, how big is the entire universe?

The short answer to the question is, that, we don’t know. If the universe is truly, mathematically, flat, it is actually infinite. But that’s a mathematical statement. What does the data say? The measurement using the spots on the cosmic microwave background radiation (CMB) found that the visible universe is flat with an uncertainty of 0.2%. But what exactly does that mean? What the measurement determined was that the curvature of the universe was zero ± 0.0020. In math, curvature is simply equal to 1/*r*. So, if curvature is zero, then the radius is infinite. But that uncertainty of 0.2% means that the curvature could be as much as 0.0020.

In order to convert that to a size, one has to invert it. So, 1/0.0020 is 500. From that, we can say that the total universe is at least 500 times bigger than the visible universe. Mind you, it might be infinite, which is what it would be if it is truly, mathematically, flat. But it’s at least 500 times bigger than we can see.

This particular observation is among the most incredible. From the size of spots on the sky, which deviate in temperature only 0.01% from average, we can leverage that information to know the minimum size of a universe that we have never seen and can never see.

This article comes directly from content in the video seriesThe Evidence for Modern Physics: How We Know What We Know. Watch it now, on Wondrium.

### The Friedmann Equation

That brings us to Einstein’s theory of general relativity that needs to be configured to represent the big bang. The equation that accomplishes this is called the Friedmann equation. The name of the mathematical model that is most commonly used is called the ‘Lambda-CDM Concordance Model’. Lambda is the parameter of dark energy that arises in Einstein’s cosmological constant model. CDM stands for cold, dark matter, which means that dark matter (whatever turns out to be) is cold, which is physics-lingo for ‘slowly moving’. It turns out that theories that assume that dark matter is moving quickly, or hot dark matter, or HDM, just don’t agree well with measurements.

In order to extract the parameters of the universe, all of the known data is compared to the equation of the Lambda-CDM model, and all of the parameters are varied. The Friedmann equation makes predictions for each value of the parameters. The set of parameters that best fits the data is the answer.

So, what are the measurements? There is a parameter that not only looks at the most likely separation between spots in the CMB, but also the third most likely separation, the fourth, etc. There are measurements of how fast the universe is expanding in the modern day, and also how fast it was expanding throughout the history of the universe. Then there are the measurements for the amount of ordinary and dark matter we see.

### Red and Dark Spots in the CMB

The red and dark spots in the CMB are instances of places where there was more or less energy in the very early universe. The CMB we see today is very far away, but the same thing happened where we are now. It happened everywhere.

Throughout the universe, those spots which had more energy eventually cooled and that led to more mass in those locations. More mass means more gravity, which pulled in matter from the surrounding cosmos. Locations with less energy had less gravity and those regions lost energy. Over the eons, the universe became patchy, with regions with more or fewer galaxies, and the size of those patches changed over time, as the universe evolved. Observations of the change of the clumpiness of the universe over time is another parameter that must be well modeled by the Friedmann equation.

### Uncertainties in Data

The data is further complicated by the fact that measurements we take today can be of objects at very different distances from the Earth, and that means that those measurements reflect very different periods in the history of the universe. It’s all very complicated. First, the equations are complex. Second, the data has uncertainties associated with it and the size of the uncertainties have to be taken into account. Data with small uncertainties are presumably better known, and they have an outsized effect on selecting the final parameters.

So, what are the parameters that have been extracted knowing the best data? It is believed that the age of the universe is 13.799 ± 0.021 billion years. The current percentage of the universe that is ordinary matter is 4.86 ± 0.10. The percentage of dark matter is 25.89 ± 0.57. And the amount of dark energy is 68.11 ± 0.62%.

### More Uncertainties

The Hubble constant is how fast the universe is currently expanding as a function of distance, is 64.74 ± 0.46 kilometers per second for every megaparsec distance from Earth. That’s the expansion rate in the modern day. Of course, since the expansion of the universe has been slowing and accelerating, this isn’t a constant number over the lifespan of the cosmos.

Other interesting parameters include how old the universe was when it became transparent, allowing us to see the CMB. It is 377,700 ± 3,200 years. That happened when the universe was 1,089.90 ± 0.23 times smaller than it is now.

### Common Questions about Cosmology and Determining the Parameters of the Universe

**Q: What is the radius of the visible universe?**

The radius of the visible universe is currently 46 billion light-years, and it reflects the absolute farthest that it would possibly be able to see.

**Q: What is Lambda a parameter of?**

Lambda is the parameter of dark energy that arises in Einstein’s cosmological constant model.

**Q: What is the age of the universe?**

It is believed that the age of the universe is 13.799 ± 0.021 billion years. The current percentage of the universe that is ordinary matter is 4.86 ± 0.10.