Sedimentary rocks from Mediterranean drought in the Messinian age as a probe of the past cosmic ray flux

We propose the use of natural minerals as detectors to study the past flux of cosmic rays. This novel application of the \textit{paleo-detector} technique requires a specific approach as it needs samples that have been exposed to secondary cosmic rays for a well defined period of time. We suggest here the use of the evaporites formed during the desiccation of the Mediterranean sea ${\sim}6$ Myr ago. These minerals have been created and exposed to the air or under a shallow water basin for ${\sim}500$ kyr before being quickly submerged again by a km-scale overburden of water. We show that, by looking at the damages left in the minerals by muons in cosmic ray showers, we could detect differences in the primary cosmic ray flux during that period, as the ones expected from nearby supernova explosions, below the percent-level. We show also that little to no background from radioactive contamination and other astroparticles is expected for this kind of analysis.