How has our understanding of the universe's shape changed over the last 100 years?

 In 1917, Einstein modeled a spherical universe where a spaceship flying straight would eventually return to its start. Discovering space's true shape took 13.8-billion-year-old light.

Einstein's static, closed model collapsed in 1929 when Edwin Hubble demonstrated that galaxies are moving away from each other, proving the universe is expanding. This discovery forced cosmologists to reconsider the shape of space. General Relativity allows for three possible geometries depending on the total density of matter and energy in the universe. If the density is high enough, gravity overcomes expansion, resulting in a positively curved, spherical shape. If the density is too low, the universe curves negatively into an open, saddle-like shape. If the density sits exactly on a mathematical knife-edge called the "critical density," the universe is perfectly flat. These different curvatures change the rules of geometry on a cosmic scale, altering how parallel lines behave and how the internal angles of a triangle add up.

The three possible macroscopic shapes of the universe depend on whether its mass and energy density is greater than, less than, or exactly equal to the critical density. Source: Wikimedia Commons.

For decades, astronomers had no way to measure which shape was real. The breakthrough came by mapping the Cosmic Microwave Background (CMB), the faint radiation leftover from the Big Bang.

In the early 2000s, space telescopes like WMAP and later Planck captured high-resolution images of the CMB. This ancient light contains tiny temperature fluctuations that formed exactly 380,000 years after the Big Bang. Because physicists know the actual physical size of these original hot and cold spots, they could use them as a cosmic standard ruler. By measuring how large the spots appear from Earth—about one degree across in the sky—they could determine how the light paths bent and warped on their journey.

If the universe were spherical, the light paths would converge, making the spots appear larger than one degree. If space were saddle-shaped, the paths would diverge, making them appear smaller. Instead, the Planck satellite data revealed that the spots are exactly the size predicted by a flat geometry. The measurements confirm that the universe is flat to a margin of error of just 0.4%, meaning on the grandest scales, Euclidean geometry holds true and parallel light rays will never intersect.

A map of the Cosmic Microwave Background taken by the Planck satellite, showing temperature fluctuations that allowed physicists to determine the flat geometry of space. Photo by ESA and the Planck Collaboration is licensed under CC BY 4.0.