From this article

During inflation there are quantum fluctuations in the inflaton field.

And this

The field φ experiences quantum fluctuations, as the uncertainty principle tells us it must.

And this

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?

  • $\begingroup$ This is a great question; we sometimes labour the point that nothing is fluctuating, but when we discuss quantum effects in classical potentials, we speak as though fluctuations are physical. $\endgroup$ – innisfree Oct 21 '18 at 7:39
  • $\begingroup$ Now I know that in some cases people use a Langevin or Fokker-Planck equation. This is the classical EoM + a stochastic term that plays the role of fluctuations. $\endgroup$ – innisfree Oct 21 '18 at 7:44
  • $\begingroup$ See eg equation 19 of arxiv.org/pdf/1505.04825.pdf. I would love to understand this more $\endgroup$ – innisfree Oct 21 '18 at 7:48

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