In 1939, George Gamow published the book “Mr. Tompkins in Wonderland”, which tells a story about a world where fundamental constants have radically different values from those they have in the real world. Gamow's classic predates modern theories that generically promote fundamental constants to dynamic entities. Constants are no longer constant. Enter Mr. Tompkins world where the speed of light c is reduced to that of a speeding bicycle, i.e. ~10,000,000 times smaller than its usual value.

In Mr. Tompkins dream, the city does not need speed limits posted, as no matter how powerful a car is, it cannot move faster than the drastically different 25-mph speed of light. This is the effect of Einstein’s theory of relativity. No need for highway patrol!

Is this Mr. Tompkins world even possible from biology perspective? We find (see our paper) that if the speed of light were reduced 10-fold, the entire Mendeleev periodic table would shrink to elements from hydrogen to sulfur. The heavier elements become unstable due to electron-positron pair emission.  In Mr. Tompkins alternative reality, where c is reduced to that of a speeding bicycle, even the hydrogen atom fails to exist.

We find several striking effects at the reduced speed of light. For example, Neon is no longer chemically inert and has the electronic structure of carbon. If the speed of light were ~10 times smaller, a neon-based life could have emerged. 

Water molecule, which is bent in our world, unfolds and becomes linear at the reduced speed of light. As such, it no longer possesses dipole moment and would cease to serve as a universal solvent, a necessary condition for sustaining life.

Life, as we know it, can only happen in a certain range of values of fundamental constants (the anthropic principle). Life is fragile.

We extend the anthropic arguments to a regime of transient variations of fundamental constants. Such regime is characteristic of clumpy dark matter models where inside the clumps fundamental constants can reach values vastly different from their everyday values. The passage of such a macroscopic dark matter clump through Earth would make Earth uninhabitable. Requiring that such a clump did not encounter Earth over the past 4 billion years (the estimated age of lifeforms on our planet), we substantially improve constraints on a certain class of dark models.

Here is our paper: arXiv:2202.04228 
Anthropic constraint on transient variations of fundamental constants
Authors: Vsevolod D. Dergachev, Hoang Bao Tran Tan, Sergey A. Varganov, Andrei Derevianko

P.S. Technically, the relevant quantity is not the speed of light, but rather the fine structure constant alpha that includes the speed of light.