## Faculty Highlight: Mustapha Ishak-Boushaki

The good news is physicists say the universe is expanding.

And they say it is expanding at an accelerating rate.

The bad news is they don’t know why this is happening.

The puzzle has placed the work of 20th century genius Albert Einstein front and center. That the universe is expanding contradicts Einstein’s initial assumption – that the universe is static or at equilibrium, neither expanding nor contracting. But Einstein included a term in the equations of his general theory of relativity to allow for a static universe, which was the prevailing thought at the time.

This brings us to newly hired UTD physics Associate Professor Mustapha Ishak-Boushaki, Ph.D., who’s conducting research “at the intersection of modern cosmology and general relativity.” In other words, he studies the large-scale universe with an emphasis on the mechanics of how the universe operates. Ishak and others trying to understand the universe’s accelerating expansion are investigating whether the acceleration is caused by “dark energy” or by modifications to gravity.

#### The dark side of the force

“The real problem is cosmic acceleration, and one of the solutions is dark energy – a new energy that we don’t know anything about but it has become something that covers all possibilities.

“It is an energy component of the universe that instead of having an attractive gravity, it has repulsive gravity. Dark energy has negative pressure. And if you take that and you put it in general relativity in the gravitation equations, it is what makes the universe accelerate,” Ishak said.

The “gravitation equations” that Ishak refer to involve Einstein’s cosmological constant, the mathematical adjustment hinted at earlier.

“In general, dark energy, or the cosmological acceleration, can be caused by the cosmological constant. This cosmological constant can be just a geometrical term in the Einstein equations and it will provide the acceleration of the universe. However, because this cosmological constant can also be related to particle physics by the vacuum energy from quantum theory, it is something that has some observable consequences.

“It [the cosmological constant] actually has a very interesting history because Einstein himself proposed it very early to make the universe not expanding. The cosmoloigcal constant would be like a constant of nature governing gravitaion. Later, [astronomer Edwin] Hubble discovered that the universe is expanding, so Einstein removed the cosmological constant. His general relativity equations do indeed produce an expanding universe,” Ishak said.

Ishak described the cosmological acceleration as a science blossoming in many directions: “It’s related to particle physics via the vacuum energy and the cosmological constant; gravitation, because of cosmology and general relativity; and it’s related to string theory and other mathematical theories that try to unify physics,” he said.

“If we try to match these equations with quanum physics, then this cosomolgoical constant is indistinguishable from vacuum energy. And there are other problems. The sign of the cosmological constant is a problem because if it is negative it would make have an attractive gravity effect. But because it is positive, it has a repulsive effect,” Ishak said.

“Dark energy and the acceleration of the universe have become the most challenging and most important problems in physics. You have the National Aeronautic and Space Administration (NASA), the National Science Foundation (NSF), and the United States Department of Energy (DOE) all putting huge amounts of money to try to understand this problem,” Ishak said.

Ishak added that the cosmological constant would be like a constant of nature governing gravitation.

“If we try to match these equations with quantum physics, then this cosmological constant is indistinguishable from vacuum energy. And there are other problems. The sign of the cosmological constant is a problem, because if it is negative it would have an attractive gravity effect. But because it is positive, it has a repulsive effect,” Ishak said.

### Expanding view of the universe

To get the big picture, look at the universe in its entirety.

“We only know 4 percent of our universe, which is baryonic matter. It is matter that we know in the laboratories. It is luminous and emits some electromagnetic radiation but is observed by our telescopes.

“The other 26 percent of all content of our universe is dark matter. We see its gravitational effect, but we don’t observe it [directly]. We see this dark matter making objects spin faster than they should, for example. And in galaxies, we see them in rotation curves. The only thing is this doesn’t radiate anything.

“In the last six or seven years we have dark energy, which is the remaining 70 percent of the universe. It also is derived gravitationally, or in other ways, and we don’t know what it is. We know that it is requested to explain many observations in the universe.

“So this is a fascinating field to work in, of course, using mathematical theories and checking them against observations, which is how we proceed in astrophysics. The accepted theory is the one that is compatible with observations,” Ishak said.

### The pull of UT Dallas

Formerly a Research Assistant and Lecturer at Princeton University, Ishak moved to Texas in August and currently teaches the physics course Mechanics and Heat.

“I have 71 students. It’s a more diversified class. And they are good kids. I graded the first exam, and, of course, I have to work very hard with them to work enough, because physics is not an easy topic. It’s the kind of material that a student assimilates from week-to-week, week-to-week. I view it like small blocks, one on top of the other. I like my students very much and I am happy with what they’ve done so far.

“Students are coming to knock on my door. We already have two graduate students and a potential third one, so things are certainly moving very nicely here.

“I plan to teach a cosmology course next spring. I already have 11 students who have expressed interest in taking the course. I expect to have a good number in there. There is a lot of excitement around that course in cosmology,” Ishak said.

In addition, Ishak said that he liked the direction the university is going and that that played a role in his coming here to teach.

“The impression I had when I first visited UTD is I felt that the floor is going up. It is a university that is going up. There is a lot of energy here. It’s not the kind of university that’s on a constant horizontal path. I felt that and I think that was an encouraging point to join UTD,” Ishak said.

### Wormholes and the space-time continuum

Ishak places his work in three “folders.”

“The first folder is dark energy and other topics in cosmology. The second folder is gravitational lensing and similar techniques. And I think my third folder of my research is classic general relativity and some of its extensions to new modern problems in cosmology. My plan is to work at the intersection of these two to find answers to open questions in modern cosmology,” he said.

Ishak describes gravitational lensing as a new technique that exploits deflection of rays of light by heavy masses to gather information about the universe.

“Very early, when Einstein proposed general relativity, one of the triumphs was that it predicted that gravity can have an effect not only on particles as we know them but can also have an effect on the trajectory of rays of light. And indeed, if there is a massive object and there is light that is passing through it, it gets deflected by that mass. That’s the basic idea of gravitational lensing. It’s deflection of light by heavy objects like galaxies, cluster of galaxies, a massive one that gives you multiple images of a background galaxy,” Ishak said.

“When combined with cosmic microwave background radiation, called the CMB, and supernovae searches, which try to measure distance as a function of the red shift of the supernovae, we have techniques that complement each other, and that’s a very precious thing to cosmology,” Ishak said.

Ishak hopes the techniques will reveal whether expansion is caused by dark energy or if it signals a new gravity theory — a discovery that would mark the breakdown of Einstein’s general theory of relativity at large scales.

“The idea [behind general relativity] is that matter content of the universe exists in a fourth dimensional space time. And this matter curves the space time. It creates that curvature of space time that tells the matter how it moves,” Ishak said.

So, matter curves space time and then the curvature of space time tells the matter where it moves?

“It’s like taking a curved piece of paper and you put a bowl that’s really round down on it,” Ishak explained. “That’s the idea, and the math of it is the math of general relativity.

“In the back of the universe you have galaxies sending light to us. The light these galaxies send travels through a very important portion of the universe. So when it arrives to us, it does have a lot of information on where it traveled. It is mathematically written in terms of the cosmological parameters. So this information can be expressed in terms of cosmological parameters, and that gives us information about different characteristics of our universe,” Ishak said.