Galactic cosmic rays (GCR) are energetic particles originating from space entering Earth’s atmosphere. They are an important source of ionization in the atmosphere, besides terrestrial radioactivity from e.g. radon (naturally emitted by the Earth’s surface). Over the oceans and above 5 km altitude, GCR are the dominant source. Their intensity varies over the 11 year solar cycle, with a maximum near solar minimum. Carslaw et al. give a nice overview of potential relations between cosmic rays, clouds and climate. Over the first half of the 20th century solar irradiance has slightly increased, and cosmic rays have subsequently decreased. RC has had many previous posts on the purported links between GCR and climate, e.g. here, here and here.
The authors concluded that this was “far too small to make noticeable changes in cloud properties based on either the decadal (solar cycle) or climatic time-scale changes in cosmic rays.” .... More studies of this kind will undoubtedly come up with different numbers, but it’s perhaps less likely that the qualitative conclusion, as quoted above, will change dramatically. Time will tell, of course.
I've written a couple of times on this topic, although admittedly the technical nature of the subject matter gets to (and beyond) the limits of my comprehension. For example, one theory linking GCRs to climate change argues that increases in solar activity (measured by sunspot numbers) drives an increase in the force/velocity of the solar wind, which in turn sweeps away Cosmic Ray particles that might otherwise reach Earth's atmosphere. Cosmic radiation in Earth's atmosphere drives ionization, which drives low cloud cover (LCC). Thus, high levels of solar activity mean low levels of sunlight-reflective LCC, from which follows an increase in global mean surface air temperatures (Global Warming).
Last year, some research was done last year by U.K. physicists T. Sloan and A.W. Wolfendale; they located short term increases/decreases in CR intensity in existing data sets (Forbush decreases, for example), and looked around for corresponding changes in LCC (low cloud cover) indexes.
They found no such increase. Israeli astrophysicist N.J. Shaviv criticized their work here, and Mr. Sloan was kind enough to respond on this very blog, here.