The paper can be found at arXiv:1006.4848, titled "Power Spectrum Analysis of BNL Decay-Rate Data" by P.A. Sturrock, J.B. Buncher, E. Fischbach, J.T. Gruenwald, D. Javorsek II, J.H. Jenkins, R.H. Lee, J.J. Mattes, J.R. Newport.
Neutrinos have a very small probability of interacting with anything. State of the art detectors are lucky to catch one neutrino for every billion neutrinos that pass through them. High energy neutrinos are more likely to react than low energy ones.
Most of the neutrinos we detect on Earth are produced in the Sun. It's commonly said that if you sent a beam of neutrinos (with the same energy as solar neutrinos) through a light-year of lead only 50% of them would be absorbed. According to theory, the universe is full of neutrinos that were created during the Big Bang, but they've been red-shifted so they now have such low energy that we don't yet have the technology to detect them.
Neutrinos are intimately connected with beta decay. All forms of beta decay emit (or absorb) a neutrino or antineutrino (some rare forms may involve 2 neutrinos, this is an area of active research). So it's reasonable to suspect that the ambient neutrino flux could affect beta decay rates... except that neutrinos are notorious for their extremely low probability of reacting.
So when that paper by Sturrock, Fischbach et al was originally announced it was greeted with a little skepticism. In the intervening eight or so years, there have not been any independent studies corroborating their findings, and the consensus appears to be that the small variations in decay rates that they found are not due to variations in the solar neutrino flux.
From https://physicsworld.com/a/do-solar-neutrinos-affect-nuclear-decay-on-earth/
Karsten Kossert, a physicist at PTB, says that his own research, with others, on decay rates has shown that there are “some fluctuations in some instrument readings”. “However, since different instruments and/or measurement techniques show different variations, we can exclude solar neutrinos as a common reason for these variations.” He adds: “In some cases, we have shown a clear correlation between environmental parameters – such as temperature, humidity, air pressure – and instrument readings.”
Kossert recently co-authored a study looking at data on decay rates from 14 laboratories around the world. The report concluded that “observed seasonal modulations can be ascribed to instrumental instability” and that “there are also no apparent modulations over periods of weeks or months”.
But even if these beta decay rate variations were due to variations in the solar neutrino flux, that wouldn't imply that the beta decay rates were radically different in the past. Remember, we're talking about rate variations of less than one percent. For decay rates to be significantly faster in ancient times would require a much higher (&/or more energetic) neutrino flux in the past, which would imply that the reaction rate in the Sun's core was much faster in the past. But that doesn't make much sense: the Sun is gradually getting warmer, not cooler. (This analysis is complicated by the fact that neutrinos travel from the solar core to its surface in less than 2.5 seconds, but it takes heat a million years or so to propagate from the Sun's core to its surface).
