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I suspect you may be misunderstanding time dilation. From the perspective of a particle, time always passes by at 1 second per second. If you yourself were to travel at relativistic speeds (relative to, say, Earth) your perspective of time wouldn't change at all. However, observers on Earth would see your "clock" to tick slower. That is, anything you do would progress more slowly from their perspective. In the very early Universe, a given particle would see most other particles moving at relativistic speeds, and so would see their "clocks" tick slower. These sorts of relativistic effects would influence interactions between particles during collisions, decay rates, etc, but are all things we know how to take into account in our models of the early Universe.