In 2010, Purdue University published a research paper stating that their researchers had detected slight fluctuations in radioactive isotope decay rates "in synch with the rotation of the sun's core." The article also stated: Has there been any further research on this, and has it been found to affect carbon dating techniques or other archeological dating methods? Graven, "Impact of fossil fuel emissions on atmospheric radiocarbon and various applications of radiocarbon over this century," Proceedings of the National Academy of Sciences 112.31 (2015): 9542-9545.
Are the fluctuations large enough to call into question currently accepted geological dates? From this article, "By 2050, fresh organic material could have the same $^$C/C ratio as samples from 1050, and thus be indistinguishable by radiocarbon dating.
It takes another 5,730 for half of the remainder to decay, and then another 5,730 for half of what's left then to decay and so on.
The period of time that it takes for half of a sample to decay is called a "half-life." Radiocarbon oxidizes (that is, it combines with oxygen) and enters the biosphere through natural processes like breathing and eating.
Some current applications for $^$C may cease to be viable, and other applications will be strongly affected." First off, the purported variations were reported to be cyclical.
So the net effect on archeological dating would be null even if these variations existed.
Scientists are not immune from "crackpot syndrome".
A bit in the other, the rate of fusion drops and the Sun collapses.
Where "A bit" is a few parts in a trillion or less, most likely very much less.
These excited neutrons then collide with nitrogen atoms in the atmosphere, changing them into radioactive carbon-14 atoms.
CARBON-14 IS ABSORBED (Figure 1b): Plants absorb this carbon-14 during photosynthesis.It is naturally unstable and so it will spontaneously decay back into N-14 after a period of time.