The Flatness of The Universe Through Theory and Observations

Understanding the universe's shape is crucial for cosmology. Whether the shape is flat not only influences many other studies based on the assumption that the universe is flat but also helps people to build a better model to explain the evolution of the universe. This paper introduces several available methods to determine its flatness, focusing on the basic ideas and related theories. The paper mainly introduces the method of using the CMB's angular power spectrum to determine the universe's shape and gives the conclusion of a flat universe. Utilizing the lambda-CDM model, which suggests a nearly flat universe. Then the paper shows other ways of using other features like redshift and geometrical properties of different types of space (open, flat, or closed) directly to measure the curvature of the universe. These methods compared to using the angular power spectrum of the CMB are less independent of the correctness of theories and models, providing a different aspect to study the shape of the universe. Although there are debates, contemporary research leans towards the conclusion of a flat universe.