It sounds plausible, but it's wrong. The accelerating expansion of the universe is not an inertial acceleration, it's the expansion of spacetime itself (it's why galaxies can have superluminal separation velocities). You'll see a Doppler-style red shift due to the velocity of separation, but no time dilation due to change of inertial frames.... even modern cosmology believes the universe is accelerating. Clocks slow with increases in velocity. So the rate clocks tick today is NOT the same rate they ticked in the past. The further one calculates back in time the faster clocks ticked and the faster decay rates occurred.
Just ask the twin who believed his decay rates were constant until he returned to the stationary frame and found out he was wrong, that his clocks had ticked slower and he had decayed slower, even though he sincerely believed he had not.
But even if this were not the case, what difference would it make if time for the whole universe ran faster or slower in the past? The rate of passing of time doesn't only affect radioactive decay, it affects everything; without something with a different inertial history to compare with, there's no way to know and it makes no difference.
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