Abstract

Is the universe finite or infinite in extent? Is it possible to see a version of ourselves in the past? If we traveled very far in one direction, would we ever return to our starting point? These questions all revolve around one big main question: What is the topology of the universe? There have been multiple efforts in trying to find a possible solution to this big question. Researchers have gathered data through various satellites such as the Cosmic Background Explorer (COBE) (1992), the Wilkinson Microwave Anisotropy Probe (WMAP) (2001-2010), and the Planck (2009-2013). These satellites had been sent into space to gather information on Cosmic Microwave Background (CMB).

CMB is the radiation that can be thought of as the ‘afterglow of the big bang’. Once the big bang was able to cool down to a point to allow atoms to form, photons were free to roam and give light in the form of radiation. Studying the CMB is one way that researchers may be able to discover the topology of the universe. Many methods have been used, and while the data researchers have collected are amazing, they have yet to lead to an answer. But there is still hope.

The goal of this portfolio is to introduce the main ideas of topology, explain what we know about the topology of the universe today and to compile resources for readers who wish to know more about the topic. This portfolio is aimed for an audience who do not have advanced knowledge in the field of Physics and Mathematics. This portfolio begins by explaining what topology is, introducing some basic 2-dimensional and 3-dimensional manifolds. From there, we will introduce 3 of the 8 Thurston geometries: Spherical, Euclidean, and Hyperbolic. With this understanding, we will be able to explore CMB and its origin. Understanding this is crucial to see why researchers have come up with the matching circles method and its results that this portfolio focuses on.