Circles in the sky
A mid–20th-century woodcut based on 19th-century mathematics provides a surprisingly accurate illustration of how our universe may have begun. The inflationary theory of the universe, developed by cosmologists including Senior Fellow Andrei Linde (Stanford University), says the universe expanded exponentially for a fraction of a second after the Big Bang, then slowed and grew into the relatively flat, uniform universe we see today.
The inflationary theory explains aspects of the universe, such as why matter clumps together into galaxies, but questions remain about exactly how to model the way the expansion took place. Linde and CIFAR Associate Fellow Renata Kallosh (Stanford University) have found that one class of models aligns closely with observational data. These models, called cosmological attractors, also have a deep mathematical relationship with a geometric model of a hyperbolic plane known as the Poincaré disk. One of the best representations of the Poincaré disk is almost as beautiful and simple as the inflationary theory itself – the artist M.C. Escher’s Circle Limit IV.
Escher, known for his infinite staircases and other mind-bending illustrations, created a series of Circle Limit woodcuts that represent infinity. In this one, rings of angels and devils become smaller and smaller as they move from the middle of the circular frame toward the outer edge, where they become crowded and infinitesimally small. In fact, the image shows perspective: they are all the same size, appearing to shrink with the distortion of space. In a recent research paper, Linde and Kallosh described how a calculation based on the geometry of the Poincaré disk represents the amplitude of gravitational waves in cosmological attractor models.
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