Does energy dilate time like mass?

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Energy in the early universe existed without mass for a brief period, raising questions about its time dilation effects compared to mass. It is debated whether this energy experienced time at a rate similar to our current experience before matter formed. As matter condensed from energy, the transition could imply a significant change in the passage of time. The concept of energy density curving space suggests a relationship between energy and time dilation. Understanding these dynamics is crucial for grasping the nature of time in relation to energy and 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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