Aside from the total solar irradiance changes, changes in cosmic rays might be the next skeptic alternative to increases in greenhouse gases and other anthropogenic activities as the cause of modern global warming. It is an idea being investiaged a lot, though some like Henrik Svensmark and Nir Shaviv are very confident that they have overturned the CO2 paradigm and found a link between cosmic rays and low level cloud cover.
A simple soda bottle experiment can demonstrate the idea…fill a 2-liter plastic bottle 1/3 full of some warm water and close the cap and swish it around such that the inside is saturated, and then squeeze the bottle in and out. Given a saturation state, you’d think you might get fog-like residue on the side. You probably won’t. Clouds need condensation nuclei to build off of, so by adding particles you enhance the water condensation process. If you light a match and let it burn for a few seconds, blow it out, and then drop it in the bottle quickly and close the cap, the smoke now can serve as a foundation for which a cloud can form. Now if you squeeze the bottle in and out, you should see some cloudiness around the sides of the bottle.
The idea behind cosmic rays is that they effect cloud condensation nuclei (CCN) and thus when you get more cosmic rays, you can get more low clouds. A decrease in CR intensity should cause a decrease in Low Cloud Cover (LCC). Changes in clouds effect the albedo of the planet.
In a new paper, by Sloan and Wolfendale, the authors investigated the link by looking for periods in time/places on the planet which had documented various cosmic ray arrivals, and seeing if that affected the cloudiness. The authors looked at solar cycles 22 and 23 especially. The conclusion by the paper is that the there is a weak correlation over the first cycle, and the upper limit percentage (less than 1/4 due to CC variability) is incompatible with a large part of the change in the LCC during solar cycle 22 being produced by changes in ionization. No correlation is found in solar cycle 23. During Forbush decreases (small decreases in CC intensity), and the causal connection would imply a decrease in LCC over a Forbush decrease, and on timescales of days and shorter. From this paper, it is statistically improbable that there is a correlation during Forbush decreases between changes in LCC and ionization.
This is a subject that needs further investigation, but no corroboration of the hypothesis of a causal connection between the changes in ionization from cosmic rays and LCC could be made in this paper. Other papers such as Benestad 2005 and Lockwood and Frohlich 2007 find no explanatory trend in cosmic rays to be causing the observed temperature rise.