Fragility of life or what would happen if the speed of light were smaller

Abstract: The anthropic principle implies that life can emerge and be sustained only in a narrow range of values of fundamental constants. We show that anthropic arguments can set powerful constraints on transient variations of the fine-structure constant alpha (or, colloquially, speed of light) over the past 4 billion years since the appearance of lifeforms on Earth. The regime of transient variation of fundamental constants is characteristic of clumpy dark matter models.  We argue that the passage through Earth of a macroscopic dark matter clump with a value of alpha inside differing substantially from its nominal value would make Earth uninhabitable. We demonstrate that in the regime of extreme variation of alpha,  the periodic table of elements is truncated, and water fails to serve as a universal solvent. Thereby, the anthropic principle constrains the likelihood of such encounters on a 4-billion-year timescale. This enables us to improve existing astrophysical bounds on certain dark matter model couplings by several orders of magnitude.