This theory was advanced by the late Dr William Gray at the Colorado State University Atmospheric Sciences Department. He was the original author of the yearly hurricane forecast so his influence was substantial. He argued strongly that climate change was due to solar cycles and so his students did a great deal of work validating this thesis.
They proved the opposite.
No matter what the sun is doing- and it doesn't change much, or life on Earth wouldn't exist in the first place- atmospheric carbon dioxide will still affect temperatures here and therefore an increase in CO² will result in higher temperatures.
Weather and climate records are bearing this out in very close agreement with projections based on increased CO² emissions.
There's another factor that's recently become a more widely recognized influence on climate and that's the high and rising levels of methane emissions. These are coming from the fossil fuel industry, primarily fracking. They're also starting to come from methane hydrates and clathrates that are dissolving as tundra and oceans warm up.
This cannot be explained away by solar cycles:
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