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We get the following picture of the formation of inhomogeneities: initially the fields (which has now decayed into well known fields of Standard model) lived in a vacuum state -- there were no real particles (only virtual ones). The fields underwent vacuum fluctuations. And there was a certain inflaton, far from being in a vacuum state.

Passing into a vacuum state (slowly sliding down according to Linde's idea), the inflaton transferred energy into the fields (somehow excited them), giving birth to real particles, but unevenly, there, in some places, more of them were born, in some less (due to the same fluctuations), but still simultaneously expanding with the Universe --- 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 got non-zero $ \Delta\rho / \rho $ at different scales.

Do I understand correctly?

Michael Seifert
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Sergio
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Contrary to popular belief, and countless popular science programmes on the subject, vacuum fluctuations do not exist. The vacuum state is not fluctuating. If you make measurements of the vacuum state you will get fluctuating measurements, but it is your measurement that is fluctuating not the vacuum state.

The density fluctuations calculated from inflationary theory are due to Hawking radiation from the event horizon caused by the accelerated expansion. During the inflationary epoch the geometry of the universe was approximately de Sitter, and in a de Sitter universe there is a cosmological horizon. This horizon produces Hawking radiation, and since this is random the intensity of the radiation varies from moment to moment and place to place. It is this that produces the density fluctuations.

A convenient reference for this is Daniel Baumann's TASI Lectures on Inflation. The calculation of the primordial fluctuations starts at section 10.1:

10.1 Quantum Zero-Point Fluctuations

As we will explain quantitatively in §12 quantum fluctuations during inflation induce a non-zero variance for fluctuations in all light fields (like the inflaton or the metric perturbations). This is very similar to the variance in the amplitude of a harmonic oscillator induced by zero-point fluctuations in the ground state; see §11. The amplitude of fluctuations scales with the expansion parameter H during inflation. This relates to the de Sitter horizon, $H^{−1}$, and the quantum fluctuations during inflation may also be interpreted as thermal fluctuations in de Sitter space in close analogy to the Hawking radiation for black holes.

Having said this I believe Sean Carroll's research group have been investigating whether there could also be randomness from a measurement like process that occurs as the inflaton field decays. I am not sure how far this has got, but in any case it is not the mainstream view. Carroll's paper is here if you want to read it.

John Rennie
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