Age of the universe
The main idea I've read over the years is that the speed of light is constant throughout space but not over time. In other words it is the same everywhere but that "same" value has been decreasing *over time* from an extremely large multiple since the universe came into being/inflated/rebounded/was created/whatever your guess is.
A much higher speed of light in the past would enable the expansion of the universe to have occurred very much (hugely in fact) quicker. If so then the universe could be fantastically younger than currently thought as it's size (which is based partly on today's light speed "constant") affects calculations of it's age and assumes the same speed of light over time.
In addition, there are many dating methods that indirectly include the speed of light in their calculations and whose results could be off by an order of magnitude on an exponential scale projected backwards over time.
These are only hypotheses but if true then the simple fact of a vastly higher speed of light in the past could lead to a young universe with a young Earth and a young fossil record.