Duke Physicists See the Cosmos in a Coffee Cup

A Duke University professor and his graduate student have discovered a universal principle that unites the curious interplay of light and shadow on the surface of your morning coffee with the way gravity magnifies and distorts light from distant galaxies. They think scientists will be able to use violations of this principle to map unseen clumps of dark matter in the universe.

Light rays naturally reflect off a curve like the inside surface of a coffee cup in a curving, ivy leaf pattern that comes to a point in the center and is brightest along its edge. Caustics also show up in gravitational lensing, a phenomenon caused by galaxies so massive that their gravity bends and distorts light from more distant galaxies. "It turns out that their gravity is so powerful that some light rays are also going to pile up along curves," said Arlie Petters, a Duke professor of mathematics, physics and business administration.

From the vantage point of Earth, the entire cosmos looks like a vast interplay of gravity and light that can extend far back into spacetime. "As with any illumination pattern, some areas will be brighter than others," Petters said. "And the brightest parts will be along these caustic curves."

Interpreting data from telescope surveys correctly requires understanding the distortions inherent in lensing, which sometimes warps a more distant point of light into multiple and magnified copies of themselves.

Petters and other researchers have previously found that, if such a light source seems to be juxtaposed within the confines of a caustic arch, two duplicate images will appear to be positioned abnormally close to each other and also seem equally bright. And because these clones are of seemingly equal brightness, subtracting one luminosity from the other results in a difference of zero.

In an article appearing in the March 23 Journal of Mathematical Physics, Petters and graduate student Amir Aazami extended the mathematics of such relatively simple examples to include what Petters called "higher order caustics." In such situations the interplay of light and gravity may extend further into spacetime and undergo various forms of "caustic metamorphosis" in the process.

The Duke researchers said that for the simplest caustics, the theorem has already been corroborated by a few actual gravitational lensing observations. And they expect the higher order caustics to be observed once the Large Synoptic Survey Telescope, now being assembled in Chile, begins what Petters called "the most massive survey of the sky known" in a few years.

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Image credit: Henrik Wann Jensen, University of California at San Diego