Lecture Notes: Cosmology and the Fate of the Universe

By Joe Linstroth

Gazing up at the night sky has a tendency to spark deep thoughts about life, perspective, and how everyone and everything got here. Add to that the study of gravitational physics and the interaction between light and matter, and that’s essentially the foundation for astronomy professor Anna Williams’s course “Cosmology and the Fate of the Universe.”

Through a blend of big philosophical questions and challenging mathematical puzzles, Dr. Williams and her students explore the knowns and unknowns of our universe and beyond.

What big questions do you ask in the course?

The two biggest questions we ask are: “How did the universe begin?” and “How will the universe end?” And in order to answer those questions, we also have to understand where we are in the universe today. We are located in the Milky Way galaxy, which is part of a local group of galaxies. It turns out this whole system is moving with a larger flow into a supercluster, which is a large group of smaller galaxy clusters. So physically speaking, we’re part of a system that is still forming the largest-scale structure in the universe.

Understanding all this requires that we collect data, which brings up other questions like: What information do we need to obtain? What physical theories and mathematics do we have at our disposal that we can use to understand the data and observations? What new tools do we need to develop? What new math? What new observations do we need to take in order to figure out how the universe began and how it’s going to end?

Cosmology is the branch of astronomy that focuses on the universe’s structure and evolution. When you’re teaching something so mind-blowing, where do you even begin?

I think a fun place to start is just asking simple questions like, “Why is the night sky dark?” If we start with a very simple understanding of the universe, for example, if we assume the universe has been around for forever and it’s not evolving—that time and space are static—then we would expect light from all the stars and galaxies to have made it to Earth today. That would mean the entire sky would be bright, but it’s not. And because of that, we know that there must be a finite age to the universe, because there hasn’t been enough time for light from all of the stars and galaxies to make it to us. There must have been a beginning.

If we can break it down into simple observations that people are used to experiencing in their everyday lives, I think that’s a fun way of grounding the students in the class and in cosmology.

What mathematical concepts do you employ in your class to examine the universe?

At the heart of cosmology, mathematically, is Einstein’s theory of general relativity. His famous theory explained various astronomical observations that we had at that time in the early twentieth century, and it’s very complicated math.

But luckily in the 1920s, the Russian physicist Alexander Friedmann found an analytical solution to Einstein’s equation, and now we have a relatively simple thing called the Friedmann Equation, which lets us think about how different forms of matter and energy in the universe affect the evolution of the universe and its expansion.

Just by manipulating one variable at a time, we can create vastly different histories and evolutionary fates for the universe. It’s quite a beautiful equation that makes it fun to keep turning the knobs and uncover all of the possible scenarios. In the end, we’re able to adjust the variables such that we have a very tidy description of the timeline of the universe we live in.

This is all pretty complicated stuff. What do students really have to work to understand?

Often when we talk about special relativity and general relativity—the idea of time dilation, that time moves differently in different frames—that is often a really fun conversation and a lot of students have to chew on those topics for a while.

The simplest way to think about special relativity is that we’ve got this speed limit, the speed of light, and it has a lot of implications for how time is measured in different frames. And then when we think about general relativity, we add in gravity and how energy affects space-time and vice versa.

What excites you about the future, in terms of advancements in technology? What mysteries could we possibly find answers to in your lifetime?

I consider myself to be an observational radio astronomer, and I’m interested in magnetic fields in galaxies, which are important when we think about a galaxy’s energy balance. They provide pressure support and accelerate particles, and so understanding what they are and what their strengths are in galaxies is important in order to really understand the full dynamical evolution of a galaxy. By observing different magnetic field strengths in different systems, we can see how they evolve on different scales. And maybe then we can backtrack to their origins.

It turns out our own Milky Way has magnetic fields that make spiral structures, and we observe these in other galaxies, but we don’t have a good understanding for how they formed or evolved. So I’m excited about the next generation of radio telescopes that are currently coming online or being proposed, like the Square Kilometre Array and the next-generation Very Large Array in New Mexico.

We use these radio telescopes to observe magnetic fields in other galaxies, and it’s amazing that we might be able to understand how they began in the universe and also how they form.