What if light had no Speed Limit? It might appear like a pointless question, as the speed of light clearly isn’t infinite, but questions like these are a good way to see how different aspects of a physical model are interrelated.
Such that, in our universe light is an electromagnetic wave. It not only has a speed, but a wavelength. If you think of a wave as an oscillation, then at boundless speed light would have no time to oscillate. So infinite light can’t be a wave. Since the wavelength of light defines its color that would also mean it has no color. But it gets worse as in classical physics light is made when electromagnetic waves cause the charges in atoms and molecules to oscillate. Deprived of waves, atoms can’t be persuaded to emit light; the universe would be a sea of darkness.
But real light in fact has both wave and particle characteristics, so let’s assume that for infinite light it’s just some kind of particle so we can still have light and color without all that interfering wave business. What else would change?
Relativity is a clear choice. Einstein’s theory of relativity rests on upon a finite speed of light. With an infinite light speed, all those fun stuffs like time dilation are thrown out the window. So is Einstein’s well-known equation, E = mc2. The main significance of this equation is that matter can be converted into energy and vice versa. It’s central to things like nuclear fusion, which powers the stars and produces the heavy elements. Stars could still be powered by gravitational contraction, but they would merely last for a million years rather than billions of years. They also wouldn’t have any mechanism to detonate as supernovae, so there would be no method to make new stars from old ones.
As Einstein’s theory of gravity is a generalization of special relativity, it’s gone too. Our model of the universe, starting with a big bang and expanding through dark energy, depends upon Einstein’s theory. Without it the universe looks very different. No dark energy, perhaps no big bang.
Of course this is all just a game of imagination. If you made different conventions about physical phenomena you would originate different effects. We have no way of experiencing what an infinite light speed universe would actually be like. But what this shows is just how interconnected different features of a physical model in fact are. Any tweak to the model has outcomes that can ripple into widely different areas, or even cause an complete model to breakdown.