From the available research, there is no convincing evidence confirming cosmic rays have a “major factor” in determining cloud cover. The ionising of air by cosmic rays will impart an electric charge to aerosols, which in theory could encourage them to clump together to form particles large enough to form cloud droplets, called “cloud condensation nuclei”.
However, the majority of physicists who research this area say such clumping has yet shown to occur. Even if it does, it seems far-fetched to expect any great effect on clouds in the atmosphere. Most of the atmosphere, even relatively clean marine air, has plenty of cloud condensation nuclei already.
It is also not even clear whether the satellite measurements of changes in cloudiness are correct or how these changes have affected temperature, as it is unknown if clouds cover may mitigate global warming or amplify it.
For the record, the Administrator of this website agrees with the findings of the IPCC assessment of the scientific, technical and socio-economic information relevant for the understanding of the risk of human-induced climate change.