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How can the energy stored in the inflaton field, an inflating substance with negative pressure (substance we’re not familiar with) decay into particles of matter and radiation that we are observing (substance we’re familiar with)?

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It's easy to confuse negative pressure for negative energy, and I wonder if this is why you think there may be a problem. The inflaton field possesses a positive energy density just like any quantum field does, and it can exchange that energy with other quantum fields to create the particles corresponding to those fields.

Well, I'm making assumptions here because we don't know what the inflaton field is or even if it really exists. There is no experimental evidence to guide us in this area. However it's widely assumed that the inflaton field is a quantum field, and behaves according to quantum field theory.

For more on negative pressure see Have negative pressures any physical meaning? This question is about dark energy, but the same reasoning applies to the inflaton field.

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