The idea that our universe may be finite but unbounded is an intriguing concept, but it's worth noting that the nature of the universe's boundary and its overall structure are still subjects of ongoing scientific investigation. That being said, there are a few pieces of evidence and theoretical considerations that have been proposed in support of a finite yet unbounded universe:
Cosmic Microwave Background (CMB) Radiation: The cosmic microwave background is the faint radiation left over from the early universe. Detailed observations of the CMB by missions like the Wilkinson Microwave Anisotropy Probe (WMAP) and the Planck satellite have provided strong evidence for the spatial flatness of the universe on large scales. This implies that the geometry of the universe is consistent with being infinite, but it does not definitively establish its overall size or boundary.
Inflationary Cosmology: Inflation is a theoretical framework that suggests the universe underwent a rapid and exponential expansion in its early moments. According to some inflationary models, it's possible for a finite region of space to expand into a much larger, unbounded universe. In this scenario, the observable universe is a small, finite portion of the overall cosmos.
Mathematical Models: Certain mathematical models, such as the Poincaré dodecahedral space, propose a finite yet unbounded universe. These models utilize non-Euclidean geometries to create a finite universe that, when traversed in any direction, eventually loops back on itself. However, it's important to note that these models are highly speculative and have not been confirmed by observational evidence.
It's essential to recognize that our understanding of the nature and structure of the universe is continually evolving. While the concept of a finite but unbounded universe is intriguing, scientists are actively researching and exploring various cosmological models to gain deeper insights into the true nature of our universe.