Fundamentals of the flatness problem

Abstract

The Flatness Problem is a fine-tuning problem (defined as when a physical constant appears to fall within an arbitrarily precise range such that the current status of the Universe was able to be developed) in physical cosmology, related to the density of matter and energy in the universe. In this paper, I provide an overview of the problem, describing the problems history, beginning with its foundations by Albert Einstein and Alexander Friedmann in General Relativity and the discoveries of Edwin Hubble and Georges Lemaitre regarding the nature and expansion of the Universe. I also present the mathematical basis of the energy density of the Universe by completing a simple derivation from the first Friedmann Equation, before analyzing observational data regarding the apparent density of the Universe. This data comes from the Cosmic Microwave Background and distant Type 1a supernovae. Finally, I explore the possible solutions to the Flatness Problem, including Anthropism and Inflation, and recount each ones strengths and weaknesses.