Unit 2: The Standard Model of Cosmology

How old is the universe and how big is it? What is the universe actually made of? Is the universe expanding? How do we know? Can we predict how fast the universe is expanding? And since the universe is so big, how do we measure distances to nearby stars and galaxies?

In this Unit, we will look at some of the basic properties of our universe to answer all of these questions. We will look at some videos, look at some equations, and write some code to make predictions about the fate of our universe. 

The Standard Model of Cosmology and the Components of the Universe

The Standard Model of Cosmology is dubbed the LCDM model and has achieved great success in modeling different epochs of our universe. Using this model, we know that the universe is approximately 13.8 billion years old. This model includes four major players which evolve in a spatially-flat universe. Here we are generally describing the role of each component. They are:

• Radiation (a.k.a. light)

• Baryons (a.k.a. regular matter, like atoms)

• Cold Dark Matter

• Dark Energy

Cold Dark Matter only interacts with the force of Gravity. It doesn't emit any light ('Dark') and is not very energetic ('Cold'). Dark Energy is even more mysterious. This component rips the universe apart making the rate of expansion grow faster and faster. Even more strangely, we think it has had a constant energy density throughout time and only (relatively) recently has it become the most dominant component in our universe. Constraints found by the WMAP mission on these components find that Cold Dark Matter is nearly five times as abundant as regular matter, Dark Energy is about 70% of the energy density today, and contributions from Radiation are vanishingly small. As you can see, the contributions of Cold Dark Matter and Dark Energy in the universe today are huge. Therefore, it's our job as cosmologists to figure out more about these mysterious components.

The Friedmann Equation

Alexander Friedmann, nearly a century ago, took a look at our standard model and created an equation which tells us how the Hubble Parameter (discussed in Unit 1) changes with time given the energy densities or mass densities of the components in the universe. As you may recall from Unit 0, a density relates to some quantity per volume. Dr. Friedmann arrived at the Friedmann equation by the principle of the conservation of energy in General Relativity: whatever energy there is in the universe at these large scales is attributed to the expansion rate of the universe. We relate the energy densities of the components of the universe to the expansion rate, where we define a few new unfamiliar parameters, as follows:

Our Standard Model of Cosmology, LCDM, takes the universe to be overall flat. This means that "k" above is equal to zero, which simplifies the equation. There are some important physical constants in here too, like the Gravitational Constant and the speed of light. 

The Critical Density: What it takes for the universe to collapse again

An important feature of this equation is that there is now a one-to-one relation between the expansion rate of the universe and the energy density of matter within it. Since gravity acts on matter and matter was the only component considered, it was reasonable to think that gravity would fight the universe's expansion and, at some point, win. After this point, the universe would collapse back in on itself. This condition will be met if the universe's mass density is equal to the critical density ⍴crit, which corresponds to when the expansion rate of the universe is equal to the matter mass density trying to collapse it. After this point, there's no going back. It's useful to compute the critical density's value today, as it simplifies the Friedmann equations a lot. 

Re-writing the Friedmann Equation in terms of the density parameters, we come to a simple expression. Note here that we separated our the individual contributions in the density parameters due to matter and due to radiation (light). This notation wasn't used when we first introduced the Fridmann Equation, where we lumped them together in one parameter, ⍴. However, this will be an important distinction in Unit 2, as these components don't evolve in the same way! We have now re-written the Friedmann equation in a much prettier way, which sums all of the contributions of the density parameters to find the Hubble Parameter at any given time.