E = hv: "God Created the Integers - The Mathematical Breakthroughs That Changed History" by Stephen Hawking
(Original Review, 2005)
Random thoughts while attempting to read the book (the edition is shitty: it's full of typos)
In EM theory, which is Lorentz invariant, there's a relation between the magnitudes of the E and B fields for light (not if you use Planck units. The magnitudes of c and h tell you nothing about physics, but a lot about biology. I don't claim that's original, BTW. I'm trying to recall who said it first, Monod or Schrödinger, E/B = c. That's quite a magnitude difference of the E over the B already. So if you could gradually increase c the structure of a light beam changes radically. But the reason for c is probably tied to quantum vacuum properties so you've got changes there too. In fact I would find it entirely reasonable not to expect invariance in E and/or B while the early universe was trying to sort out its equilibrium conditions during falling out of the gravitational, electromagnetic, weak forces just after the BB.
If you're into stuff like this, you can read the full review.