Looking at a flux vs. time graph of secondary cosmic rays (e.g. from a neutron station: www.nmdb.eu/nest/search.php can plot you some. I just tried for example Moscow, from 14 Oct 1951 to today, scaling options $\to$ Specify your own Y axis scale -20,20, left untouched all other options), it's easy to see a periodicity that fits well with the solar 11 - 22 year cycles.
So, why do solar cycles influence the rate at which cosmic rays hit the Earth?
I suspect the reason is so well known among experts that is not mentioned in the introduction of the first random article about this I looked for. Maybe you know a nice, simple book/review article?