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During inflation there are quantum fluctuations in the inflaton field.
The field φ experiences quantum fluctuations, as the uncertainty principle tells us it must.
However, the field φ, like every other field, is subject to quantum mechanical fluctuations. As it rolls down the hill, in some regions φ fluctuates downwards and in others it fluctuates upwards.
This answer states that the fluctuation is in the measurement of the field not in the field itself. Quantum fields do not fluctuate. That is, there’s no quantum fluctuations causing the field value to fluctuate.
What is really meant by “quantum fluctuations” in the inflaton field? Fluctuations from what? $~$How does it cause the inflaton field to fluctuate to a higher field value in some regions and to a lower field value in some others?