Cosmological Fundamentals

This is part one of a two part series on the Big Bang theory. Here we cover the foundational concepts used in the benchmark model we cover in part 2. We start out with the basic Cosmological Principles for an isotropic and homogeneous Universe. We then review Hubble’s Law that came from the discovery that the Universe was expanding. We go into some depth to illustrate what expanding space is and how it impacts the basic idea of ‘distance’. This includes a definition of Cosmic Distance and how it leads to the Visible Horizon.  We then develop a concept of how the Universe’s expansion would work using Newton’s gravitational theory including his Shell Theorem. We use this to define a cosmic scale factor and use it to see what happens in a matter dominated Universe. We then expand that to include a radiation dominated Universe. With the Newtonian mechanics view in hand, we update to Friedmann’s equation based on Einstein’s General Theory of Relativity along with the Equation of State. We examine the impact of flat, spherical and hyperbolic space on the cosmic sale factor, and identify the Critical Energy Density needed in order to have flat space. We end with a look at cosmological redshift, and an observation on galaxy counts that lead to the conclusion that we exist in flat space-time.