According to theory, radioactive elements will always at a constant rate, with a little variability due to randomness. What you should not expect to find is that the rate of decay changes with the distance of the Earth from the Sun.
In pre-Calculus, we’re figuring out how to match curves to data. The scientists in this study do something similar, trying to see what types of sinusoidal curves will match the data, then seeing what natural phenomena have the same period (the time it takes for one cycle).