In cosmology, the terms "curved," "flat," and "open" are used to describe different possible geometries of the universe based on its overall curvature. These concepts are derived from the mathematical framework of general relativity and the study of the universe's large-scale structure.
Curved Universe: A curved universe refers to a geometry where spacetime is curved, similar to the surface of a sphere. In this case, the sum of the angles of a triangle would be greater than 180 degrees. A positively curved universe is often referred to as a closed universe because it is finite but without boundaries. It means that if you travel in a straight line in any direction, you would eventually return to your starting point. However, observations indicate that our universe is not positively curved.
Flat Universe: A flat universe corresponds to a geometry where spacetime is flat, similar to a sheet of paper. In this case, the sum of the angles of a triangle is precisely 180 degrees. A flat universe has infinite spatial extent and is often associated with a critical density of matter and energy. Observational evidence, including measurements of the cosmic microwave background radiation, suggests that our universe is very close to being flat.
Open Universe: An open universe refers to a negatively curved geometry, like the surface of a saddle. In this case, the sum of the angles of a triangle is less than 180 degrees. An open universe has infinite spatial extent, but unlike a flat universe, it expands at an accelerating rate. Observational data, including measurements of the cosmic microwave background and the distribution of galaxies, suggests that our universe is consistent with being open and negatively curved.
It's important to note that these descriptions are based on the prevailing cosmological models, such as the Lambda-CDM model (Lambda refers to the cosmological constant, and CDM stands for Cold Dark Matter), which provides the best fit to observational data at present. However, our understanding of the universe is constantly evolving, and future discoveries may refine or revise these concepts.