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.