Does energy dilate time like mass?

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If I understand it, in the very early universe there was only energy and no mass, I guess for only a fraction of a second.

Did that energy have the same time dilation effect as the mass it became?

If not, was time passing at a rate similar to what we experience right now and then suddenly hit the brakes as matter condensed out of the energy? If you suddenly have the mass of the universe in a relatively small region, it seems like time would practically stop.
 
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