Warum ein flaches Universum immer noch 18 mögliche Formen zulässt

Cosmologists are fairly certain the universe is flat, yet this observation leaves a massive range of possibilities for its true shape. While a flat geometry implies Euclidean rules, it doesn't dictate whether space extends infinitely or wraps around itself in complex, finite ways.

The limits of triangulation

Carl Friedrich Gauss famously explored geometry by measuring the angles between mountain peaks like Hohenhagen, Brocken, and Inselberg. He found the sum of the angles was close to 180 degrees, suggesting a flat plane. However, using triangles to map the cosmos is fundamentally broken at scale. Stars in neighboring galaxies are too close to provide a meaningful baseline against the vastness of the universe, and gravity itself curves the paths of light, muddying the measurements.

To find the truth, researchers look back 13.8 billion years to the cosmic microwave background (CMB). This light, released roughly 370,000 years after the Big Bang when the universe became transparent, carries the signature of the early primordial soup of quarks and gluons. The CMB is remarkably uniform, supporting the cosmological principle that the universe is both homogeneous and isotropic.

Decoding density fluctuations

Einstein’s equations of general relativity dictate that if the universe is homogeneous, its curvature must be constant. This limits the possibilities to three primary cases: zero curvature (Euclidean), positive curvature (spherical), and negative curvature (hyperbolic). We can distinguish these by looking at the size of density fluctuations within the CMB. If the universe were positively curved, these fluctuations would appear larger than they are; if negatively curved, they would appear smaller.

Even if the data confirms zero curvature, the topology remains an open question. A flat universe could be an infinite Euclidean plane, or it could be a three-dimensional generalization of a donut's surface. Mathematics suggests there are 18 distinct ways a flat space can be configured, ranging from simple infinite expanses to complex, finite, wrapping structures. Determining which of these 18 shapes defines our reality remains one of the most significant challenges in modern cosmology.

Source: The universe could have 18 possible shapes
Domain: scientificamerican.com