After publishing his theory of general relativity, Einstein turned his attention to the universe. In 1917, he proposed a cosmological model based on general relativity that challenged traditional beliefs, introducing the concept of a finite yet unbounded universe. Previously, people thought that being finite meant having boundaries, while the infinite was considered boundaryless. However, Einstein distinguished between these two concepts and introduced the idea of a finite but unbounded universe.
For example, consider a rectangular tabletop; it is finite but has boundaries. Similarly, the surface of a basketball is finite yet unbounded. These examples help illustrate Einstein's theory. According to cosmological principles, three-dimensional space is homogeneous and isotropic on a cosmic scale. Einstein believed that such space must be a space of constant curvature, meaning the degree of curvature is the same everywhere. Thus, he envisioned a three-dimensional hypersphere as a model of the universe. This hypersphere is finite and unbounded, allowing humans living within it to move in any direction without encountering a boundary.
Einstein attempted to solve this model using the field equations of general relativity, but the lack of initial and boundary conditions made the solution process quite complex. To simplify the equations, he assumed that the universe was finite, unbounded, static, and had uniform isotropy. Nevertheless, he found that general relativity could not directly lead to a conclusion about a static universe. Therefore, Einstein introduced a 'cosmological constant,' or cosmological term, to derive a static, homogeneous, isotropic, finite, and unbounded model of the universe. This discovery caused a significant stir, as it seemed the scientific community had found an answer to whether the universe is finite or infinite.
