What is the origin of spatial inhomogeneities in the Universe?

[sergiokapone]

We get the following picture of the formation of inhomogeneities:

Initially, all eternally existing fields (possibly fermionic-lepton-quark-DM-field and GUT-field) lived in a vacuum state --- no real particles (only virtual ones), just fluctuated ($\left\langle\Delta E\right\rangle = 0$, $\left\langle\Delta E^2\right\rangle \neq 0$ ). And there was an inflaton, far from being in a vacuum state (why would? Others in a vacuum). Passing into a vacuum state (slowly sliding down as Linde wants), the inflaton transferred energy to the fields (somehow excited them) and born particles clumbs in places of fluctuation, but still expanding along the way - these clumps of real particles were stretched, but new clumps still continued to be born in those places where the fields fluctuated with the extraction of energy from the inflaton. We obtained nonzero $\Delta\rho/\rho$ at different scales, and it was these inhomogeneities in real particles in space (not virtual) that were further condensed due to gravity into clusters, galaxies, stars ...? So I understand?

 

[kimbyd]

I don't think it's a matter of the inflaton transferring energy to other fields. The energy in other fields was driven rapidly to zero by inflation. Rather, as the universe expanded and the inflaton approached its potential energy minimum, the value of the inflaton field itself fluctuated, descending slightly faster in some regions than in others.

When it reached its minimum, the inflaton field decayed rapidly into standard model particles (reheating). The very slight differences in the field value from place to place due to the initial fuctuations result in different densities once reheating is finished.

 

[PeterDonis]

I don't think it's a matter of the inflaton transferring energy to other fields.

At the end of inflation, it is, as you say later in your post:

When it reached its minimum, the inflaton field decayed rapidly into standard model particles (reheating)

I think the key thing the OP appears not to have grasped here is that reheating is not a continuous process that goes on during inflation; it is a very rapid process that happens at the end of inflation.