It is believed that quantum fluctuations in the inflaton field caused inflation to end at different times in different places, which led to CMB fluctuations (1 part in 100,000).
Eternal inflation also relies on quantum fluctuations in the inflaton field causing inflation to end at different times.
But the fluctuations in the CMB are tiny and the fluctuations in eternal inflation are large. $~$Are quantum fluctuations in these two scenarios really the same process?
It is believed that quantum fluctuations in the inflaton field caused inflation to end at different times in different places, which led to CMB fluctuations (1 part in 100,000).
These are fluctuations in space also , i.e. space time, these fluctuations are considered the seeds of the clusters of galaxies in our observable universe.
Eternal inflation also relies on quantum fluctuations in the inflaton field causing inflation to end at different times.
These times in the models are outside our observable universe's spacetime.
However, the quantum fluctuations necessary to explain structure do not act solely at lowish inflaton field values. They act at higher field values as well, and in the so-called "large field" models that I'm focusing on here the fluctuations' strength grows as the field value increases. So the fluctuations should be taken into account for the entire history of the field, and then it seems that "eternal inflation" may occur. Here a runaway situation occurs with regions that fluctuate uphill inflating faster, allowing growing physical volumes of space to sustain inflation forever.
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We would live in a rare region where inflation ends
These space volumes, in contrast to our observable universe, are still supposed to be in a quantum mechanical state, they have not been transmuted, because of their large values, into the generation of quarks gluons etc and the final decoherence coming from this manifestation that generated our observable universe. The hypothesis is that the quantum mechanical state would continue for ever in regions where the inflaton field fluctuated to high values, not allowing the generation of a universe like ours. (or even more paradoxical situations , read the link)
In this plot we see our observable universe, and the quantum fluctuations that resulted to this history are shown before 10^-32 seconds in the development.
The hypothesis that leads to eternal inflation is that quantum fluctuations, need not be only of a relatively small size in energy variations which lead finally to the formation of matter in our universe. Another path would be to assume that as they are fluctuations, they could be so large that there would be no chance for the expansion to cool enough to enter the quark era and proton formation. These would be alternate paths, outside our observable universe, that would lead to eternal inflation according to the link. We are just lucky to live in a livable universe. The CMB is our observable universe's CMB. The alternate paths outside our observable universe will not have a CMB because particles never emerge due to lack of enough cooling.
You add:
But the fluctuations in the CMB are tiny and the fluctuations in eternal inflation are large.
The CMB is a picture captured at 380.000 years after the creation of our universe, when the photons decoupled. The fluctuations in the CMB have a small probability, they are not tiny, as they are the seeds of clusters of galaxies; and they are just a picture of the matter concentrations that were seeded by the inflaton field building our observable universe. The alternate universes have no CMB.
Are quantum fluctuations in these two scenarios really the same process?
Well, it will depend on the model, one can generate a gamut of quantum mechanical fluctuations, small that can lead to universes like ours, and large that would lead to eternal inflation. In this sense they are the same process.
