Joshua Foster’s long-standing interest in computational tools is, he believes, what led him to research a range of theoretical physics, including dark matter, gravitational waves, and new physics. “What got me interested in studying theoretical physics in particular was the idea that you could study structures or ways of doing calculations that would enable you to make predictions or derive results that just wouldn’t have been possible with previous approaches,” he says.

Foster, who referred to himself “extremely Midwestern,” grew up in Indianapolis, attended Indiana University as an undergraduate, and the University of Michigan for his PhD. He joined MIT as a Pappalardo Fellow in the Center for Theoretical Physics, then Fermilab as a Schramm Fellow in Theoretical Astrophysics. In August 2025, he joined the UW–Madison physics faculty.

Please give an overview of your research.

I’m generally interested in problems that surround: 1) the optimal design of an astrophysical observation or a laboratory-based experiment, 2) serious phenomenological calculations that give us a good understanding of what a signal of new physics might look like, and 3) the application of statistics and data analysis to determine if new physics signals were hiding in data that was accessible to us all along.

My primary interest, at least historically, has been in dark matter. At present, all we can really say is that 85 percent of the matter of our universe is yet to be identified, so it seems like a rather urgent problem to understand what that is. It also seems to be one of the few unambiguous hints of new Physics. My research is generally focused on what often is referred to as indirect and direct detection. The idea behind indirect detection — meaning that dark matter or other signals of new physics might appear to us in astrophysical datasets — is that although it might be challenging directly observe dark matter or new physics phenomena, we might be able to observe its downstream effects in astrophysical contexts. For example, dark matter could be made up of particles that annihilate when they encounter one another, and doing so produces gamma-ray signals. Or, dark matter could convert to photons in extreme astrophysical environments, producing radio signals. I’ve been thinking a lot about how to perform optimal searches in radio data in the search of that data. Another possibility is, we say, okay, these systems are interesting but complicated and intrinsically messy. Then we might alternatively look for dark matter interactions with precision laboratory systems. That’s the two-pronged big picture: looking for new physics in astrophysical observables and looking for physics in laboratory-based searches.

Then lately I’ve been thinking quite a bit about gravitational waves, which I find exciting because they might let us probe the mysterious early universe. We typically look back in time by looking at photons that are coming to us from a very, very long time ago. There’s a certain time we can’t look past, which is when the universe was too opaque to photons, but gravitational waves should have freely propagated through the universe, providing us with a way of looking even further back in time. It might be our best chance at understanding the physics of the very highest scales that would have been active in the early universe.

What are the first one or two projects your new group will work on here?

A major focus of my research going forward will be on detection strategies for gravitational waves. One exciting possibility that I’ve been studying recently is that the roughly 60 years of lunar laser ranging data — high precision measurements of the Earth-Moon distance — could be used to detect gravitational wave backgrounds at frequencies that have been challenging to access by other technologies. In tandem, it’s nice to understand what the new physics theories are that can generate gravitational wave signals, either at the frequencies that we can access with lunar laser ranging or at the frequencies that are being accessed currently by, for example, pulsar timing arrays, but might also be accessed in the future by the upcoming LISA observatory. And so really understanding how to make optimal use of the data that these observatories are collecting and how to connect them with new ideas for how models of new physics can generate gravitational wave observations is something that I plan to focus on.

In conjunction, I am looking for radio signals of axions, which convert to photons in the strong magnetic fields which surround neutron stars. The facilities and technologies through which we can perform radio observations are constantly being improved and eventually are going to culminate in two upcoming observatories: DSA-2000 and the Square Kilometer Array. As we prepare for these upcoming facilities, there are both prototypes and pathfinder observatories that are collecting data right now. So I’m interested in using those existing datasets to, first off, perform searches that are already going to have reach unparalleled by any others, and to set the stage for future data collections and analysis efforts with these upgraded facilities.

What attracted you to Madison and the university?

Well, having begun this conversation by saying I’m very Midwest—I wanted to come back to the Midwest. And the department here has people with a broad set of expertise in many different technical fields that are all of interest to me. For example, in these contexts where I’m thinking about axion-photon interactions around neutron stars, the great challenge is understanding this complicated astrophysical environment. Here, there are experts in plasma physics, and there’s WIPAC, which is this incredible particle astrophysics center. The connections across campus in terms of the emerging data science focus also made me feel like this was a place where I would have colleagues with strong overlapping interests.

What is your favorite element and/or elementary particle?

I like helium. We can use helium-3 and helium-4 to make things very, very cold, and many of the experiments that I like to think about require extraordinarily cold systems to minimize thermal noise. They are only possible thanks to dilution refrigerators that pump helium in a manner that allows it to reach temperatures as low as 10 millikelvin. And Helium-3 has a number of other, to my mind at least, magic quantum properties. The number of interesting things that you can do with helium-3 seems to be limited only by your imagination.

My favorite particle is the axion. It’s my favorite dark matter candidate. And it might not exist in nature, but it is my favorite hypothetical particle. I hope it exists and that we find it.

What hobbies and interests do you have?

Cooking is my primary hobby. I like to eat—that’s part of it. But one of the joys of cooking is that you get to spend time on a craft. You can develop a skill and expertise, and you can measure your progress over time, and at the end of it, you eat the thing that you made, and then move forward with your life unburdened by your act of creation. So it’s also very low stakes.  Other than cooking, I like to hike and I like to read.