Did cosmic radiation affect mankind significantly?

Some of my previous posts referred to the following claims by various authors of renown.
• Rock and cave art suddenly appeared about 35,000 years ago.
• About 37,000 years ago, advanced toolmaking, music and art appeared to flourish.
• Humans were born with larger brains. This may have given them some advantage relative to earlier humans, such as more complex thinking, without necessarily equating to an increase in intelligence.
• Cro-Magnon humans appeared suddenly. They were like modern people.
• Dogs were domesticated from gray wolves.
• Sophisticated speech may have arisen.
• Massive extinctions of humans and other life forms occurred.

A major flood of cosmic radiation, occurring about 41,000 years ago, has been suggested as the cause of the above developments through genetic mutation. It takes only about 2,000 years (about 70 generations) for the survivors to display new characteristics; and to propagate them into posterity.

Other bursts of radiation have been postulated at 34,000 years, 16,000 years, and 13,000 years ago. These would have caused more radiation, while contributing to yet more genetic mutation.