Cosmic Triangles Open a Window to the Origin of Time

In late August, paleontologists reported finding the fossil of a flattened turtle shell that “was possibly trodden on” by a dinosaur , whose footprints spanned the rock layer directly above. The rare discovery of correlated fossils potentially traces two bygone species to the same time and place. “It’s only by doing that that we’re able to reconstruct ancient ecosystems,” one paleontologist told The New York Times.Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research develop­ments and trends in mathe­matics and the physical and life sciences.The approach parallels the way cosmologists go about inferring the history of the universe . Like fossils, astronomical objects are not randomly strewn throughout space. Rather, spatial correlations between the positions of objects such as galaxies tell a detailed story of the ancient past. “Paleontologists infer the existence of dinosaurs to give a rational accounting of strange patterns of bones,” said Nima Arkani-Hamed, a physicist and cosmologist at the Institute for Advanced Study in Princeton, New Jersey. “We look at patterns in space today, and we infer a cosmological history in order to explain them.”

One curious pattern cosmologists have known about for decades is that space is filled with correlated pairs of objects: pairs of hot spots seen in telescopes’ maps of the early universe; pairs of galaxies or of galaxy clusters or superclusters in the universe today; pairs found at all distances apart. You can see these “two-point correlations” by moving a ruler all over a map of the sky. When there’s an object at one end, cosmologists find that this ups the chance that an object also lies at the other end.

The simplest explanation for the correlations traces them to pairs of quantum particles that fluctuated into existence as space exponentially expanded at the start of the Big Bang . Pairs of particles that arose early on subsequently moved the farthest apart, yielding pairs of objects far away from each other in the sky today. Particle pairs that arose later separated less and now form closer-together pairs of objects. Like fossils, the pairwise correlations seen throughout the sky encode the passage of time—in this case, the very beginning of time.
Cosmologists believe that rare quantum fluctuations involving three, four or even more particles should also have occurred during the birth of the universe. These presumably would have yielded more complicated configurations of objects in the sky today: triangular arrangements of galaxies, along with quadrilaterals, pentagons and other shapes. Telescopes haven’t yet spotted these statistically subtle “higher-point” correlations, but finding them would help physicists better understand the first moments after the Big Bang.
Yet theorists have found it challenging even to calculate what the signals would look like—until recently. In the past four years, a small group of researchers has approached the question in a new way. They have found that the form of the correlations follows directly from symmetries and other deep mathematical principles. The most important findings to date were detailed in a paper by Arkani-Hamed and three co-authors that took its final form this summer.

This Hubble Space Telescope image contains about 5,500 galaxies in a region of sky a small fraction of the diameter of the full moon. Cosmologists find that galaxies exhibit a nearly scale-invariant two-point pattern; hold a ruler of any length up to the sky, and if there’s a galaxy at one end, this increases the chance of a galaxy also lying at the other end.Photograph: NASA