I read recently on the internet that the speed of light early in the expansion process, post-Big Bang, may have been greater than the speed of light now. How is that possible, and if true, what are the general implications for our understanding of the basic scientific principles we live by now?
The article was in yahoo's science news section sometime last week. Close as I can get, sorry.
It seems like the article you read was only one of many which reviewed a paper sent to the journal Nature this month. The New York Times and CNN.com also both carried a similar article (based on your description - I could not find the one from Yahoo).
The article in Nature talks about the possibility of the speed of light changing over the history of the universe. Where this stems from is observational evidence that the "fine structure constant" has changed. The fine structure constant determines the exact wavelength of fine structure lines in the spectra of atoms, and measurements of the spectra of quasars suggest that it many have decreased by 0.00072 +/- 0.00018 % over the past 6-10 billion years (ref in the Nature article).
The authors of the paper argue that since the fine structure constant is equal to the charge on an electron squared divided by Planck's constant times c (speed of light), then for the fine structure constant to change one of these must also change. They go on to provide an arguement as to why they think it much be the speed of light, and that's what caught the eyes of the popular press.
However this article out today on the LANL preprint server argues why dimensionful constants (like c) cannot change, since we can just define them to be whatever we want by changing units. For example if we define units in which the speed of light and Planck's constant are both exactly equal to one (which is commonly done in theoretical Physics), then the fine structure constant is just equal to the charge on an electron squared, and the question has no meaning.
Update: Since then more debate has followed and no consensus has been reached yet by scientists. It's very interesting though. You can read more about some of the implications in this answer.
This page was last updated June 27, 2015.