For decades, astronomers have been exploring the idea that the universe might have a specific shape or structure on the largest scales, which could influence how space is connected. This area of study is called cosmic topology, and it suggests that, in some scenarios, a traveler could move in a straight line and eventually return to their starting point in space, though not necessarily in time. This hypothetical scenario involves what's known as a "closed timeline curve," or a time machine. While the current scientific consensus assumes the universe is flat and extends infinitely in all directions, cosmic topology challenges this view by suggesting the universe might have a more complex, finite shape. Cosmic topology involves the possibility of non-shrinkable closed loops—paths that, if followed far enough, could bring a traveler back to their original location. Scientists like Andrew Jaffe, a professor of cosmology and astrophysics at Imperial College London, are working to detect the signs of such a structure using large-scale observations of the universe. These signs might be visible in the cosmic microwave background (CMB), the oldest light we can observe, or in the way matter is distributed throughout space. The CMB, emitted about 380,000 years after the Big Bang, has been studied since the 1960s, but only recently have scientists had the technology to detect subtle patterns that could hint at the universe's shape. The study of cosmic topology gained momentum in the late 1990s when scientists realized that patterns in the CMB could be used to search for such structures. Missions like the WMAP satellite in the mid-2000s and more advanced observations in the 2010s have provided more detailed data. In recent years, Jaffe and a group of international researchers formed the COMPACT collaboration to explore these ideas further. Their work is beginning to develop the full mathematical framework to understand the possible shapes the universe might take. To fully understand the universe's topology, scientists would need a detailed three-dimensional map of the cosmos, which would involve studying galaxies, gas, and galaxy clusters using the most powerful telescopes available. One potential clue is the existence of "identifications," where distant parts of the sky might actually be close together in a curved space. This could result in repeated patterns, such as a circle in one part of the sky matching exactly with a circle in another. Jaffe compares this idea to a three-dimensional doughnut shape, where moving in certain directions could loop back to the same point. While these topological features might exist, they could be difficult to detect. For instance, if the universe is shaped like a torus, the scale might be too vast to observe both ends simultaneously. Even with the best technology, such large-scale structures may remain beyond our reach. However, existing data or future observations of the CMB and the distribution of galaxies might provide the answers. Understanding the universe's size is key—if it is much larger than the distance to the CMB, we may never be able to detect its true shape.