Einstein's Field Equation
Just as retrograde motion of the planets shows that Earth is not the centre, the Cosmic Microwave Background is first-hand evidence that c has changed. When we get our heads out of over-analysis and look at it, the average temperature appears the same over large areas. Large regions of Space were able to reach thermal equilibrium. Even at this time of recombination 300,000 years after the Big Bang, the speed of light was much faster.
One book everyone should take to bed (at least until my book is released) is called RELATIVITY: THE SPECIAL AND GENERAL THEORY by someone called Albert Einstein. It lists at only $6.95 US, far less than the $100+ book your professors forced you to buy. No one understood Relativity like Einstein himself. Einstein's mathematical techniques are different and more insightful than the shortcuts used today. The books written by others fail to capture Einstein's understanding of Theory.
In Chapter 31 Einstein attempts to envision the entire Universe. He concludes that the most logical shape is a sphere of 4 dimensions. His theory also predicted that a spherical space would collapse due to gravity. Einstein introduced a "cosmological constant," a repulsive force counteracting gravity. Later he called that his "greatest blunder." We shall not repeat that blunder.
When you have finished that book, move on to THE MEANING OF RELATIVITY for a more detailed mathematical treatment. In the appendix for the second edition, on page 117, he restates the field equation of gravitation, the "Einstein equation."
Here we see that R = ct and GM = tc^3 form a solution to the field equations of gravitation. Any cosmology should solve the Einstein-Friedmann equations. Since this Universe with a changing speed of light also fits the data, there is reason to be optimistic.