Radiation can cause damage to DNA. Errors that occur when this damage is repaired can lead to mutations and rearrangements in the DNA, which are the genetic diversity that is required for evolution.
The cosmic particles (including muons) move through your body and sometimes they interact with one of your atomic nuclei. The typical energy deposited by a dark matter particle is of the order keV. This is very small for nuclear energies, and thus the nuclei themselves are not affected, they just wiggle a bit. But it is an energy much larger than the energy necessary to break molecular bonds, which is typically about a factor 1000 smaller.
These dark matter particles thus can damage the bond structure of molecules inside your body. So, just by chance sometimes dark matter will damage your DNA. Most of the time this happens the damage will be repaired or the cell will die. But sometimes it won’t; sometimes, the damaged DNA can live on and reproduce.
The dark matter detectors presently operating contain something between 50 and 250 kg of mass, so for a theoretical physicist that’s the average spherical cow. These detectors have an expected number of events between a handful and some thousand per year.
Hi Lisdelys, the effect of cosmic particles on evolution is probably negligible because there are so many other earthly factors that have a more profound effect on our DNA.
Look at animal genomes. They are riddled with retroviral elements, transposons, repeating sequences, etc. (formerly called junk DNA).
True, cosmic particles can cause point mutations, but wholescale gene rearrangements have a more terrestrial explanation.