One hundred years ago, Einstein re-envisioned space and time as a rippling, twisting, flexible fabric called spacetime. His theory of general relativity showed how matter and energy change the shape of this fabric. One might expect, therefore, that the fabric of the universe, strewn with stars, galaxies, and clouds of particles, would be like a college student’s dorm room: a mess of rumpled, crumpled garments.
Indeed, if you look at the universe on the scale of stars, galaxies, and even galaxy clusters, you’ll find it puckered and furrowed by the gravity of massive objects. But take the wider view—the cosmologists’ view, which encompasses the entire visible universe—and the fabric of the universe is remarkably smooth and even, no matter which direction you turn. Look up, down, left, or right and count up the galaxies you see: you’ll find it’s roughly the same from every angle. The cosmic microwave background, the cooled-down relic of radiation from the early universe, demonstrates the same remarkable evenness on the very largest scale.
A computer simulation of the ‘cosmic web’ reveals the great filaments, made largely of dark matter, located in the space between galaxies. By NASA, ESA, and E. Hallman (University of Colorado, Boulder), via Wikimedia Commons
Physicists call a universe that appears roughly similar in all directions “isotropic.” Because the geometry of spacetime is shaped by the distribution of matter and energy, an isotropic universe must posses a geometric structure that looks the same in all directions as well. The only three such possibilities for three-dimensional spaces are positively curved (the surface of a hypersphere, like a beach ball but in a higher dimension), negatively curved (the surface of a hyperboloid, shaped like a saddle or potato chip), or flat. Russian physicist Alexander Friedmann, Belgian cleric and mathematician Georges Lemaître and others incorporated these three geometries into some of the first cosmological solutions of Einstein’s equations. (By solutions, we mean mathematical descriptions of how the three spatial dimensions of the universe behave over time, given the type of geometry and the distribution of matter and energy.) Supplemented by the work of American physicist Howard Robertson and British mathematician Arthur Walker, this class of isotropic solutions has become the standard for descriptions of the universe in the Big Bang theory.
However, in 1921 Edward Kasner—best known for his coining of the term “Googol” for the number 1 followed by 100 zeroes—demonstrated that there was another class of solutions to Einstein’s equations: anisotropic, or “lopsided,” solutions.
Known as the Kasner solutions, these cosmic models describe a universe that expands in two directions while contracting in the third. That is clearly not the case with the actual universe, which has grown over time in all three directions. But the Kasner solutions become more intriguing when you apply them to a kind of theory called a Kaluza-Klein model, in which there are unseen extra dimensions beyond space and time. Thus space could theoretically have three expanding dimensions and a fourth, hidden, contracting dimension. Physicists Alan Chodos and…