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I've heard that fluctuations in the CMB provide support for inflationary theory, as they are thought to be amplified quantum fluctuations of the inflaton field. My question is, what is so "quantum" about these fluctuations? To put it more concretely, can they really be used to provide a measurement of $\hbar$ if you don't know the details of the inflaton physics, or is there some sort of uncertainty principle associated with the fluctuations that makes them quantum and not classical?

Edit: I think I am close to considering this answered, but it may help if I give a clarifying example.

If you take a hot photon mode (though any harmonic oscillator would work just as well), it will have mostly thermal fluctuations in the observed values of the electric and magnetic fields (with typical caveats about needing to prepare the same state many times to make many measurements). If you then cool it down, the fluctuations will decrease and decrease until they reach a scale associated with inherent quantum fluctuations of the ground state. Importantly, if you only measure, say, the electric field, then quantum mechanics doesn't dictate any limit on the fluctuations of the E-field alone (you can shrink the E-field fluctuations all you want at the expense of increasing the B-field fluctuations). So I don't think "small" fluctuations can really be a signature of quantumness unless there's some complementary observable which has correspondingly big fluctuations, in a quantitative relationship that ultimately should involve $\hbar$.

I think what the answers are saying is that the fluctuations thought to give rise to CMB structure are not the same kind of thing. It's not about distinguishing ground state fluctuations from thermal fluctuations, rather these are associated with a length scale (presumably the Planck length?) which is inherently quantum, is that the idea?

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    $\begingroup$ is there some sort of uncertainty principle associated with the fluctuations that makes them quantum and not classical? The inflaton field is assumed to be a quantum field. All quantum fields have uncertainty relations. $\endgroup$
    – Ghoster
    Jun 20, 2023 at 5:33
  • $\begingroup$ So by "hot photon mode", I guess you mean a thermal source of photons, right? $\endgroup$ Jun 21, 2023 at 3:21
  • $\begingroup$ Yes, that's right! $\endgroup$
    – Munthe
    Jun 21, 2023 at 8:08

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Quantum fluctuations are the only known way to produce fluctuations small enough so as to be amplified by 10^30 to see what we see today as the ~1.8E-4 Kelvin fluctuations around the 2.7255K average of the perfectly random, isotropic and gaussian distribution (indistinguishable from a theoretical curve) of temperatures in the CMB.

The fact that the CMB shows tiny fluctuations in temperature is strong evidence that the universe underwent a period of inflation. If the universe had not undergone inflation, we would not expect to see a CMB, or if it had inflated more slowly, we would expect the matter to be spread out more evenly, and to see the CMB to be more uniform - although there is some controversy around this - the magnitude of variation could also have been much higher. Wikipedia has an incredible article about this, including a timeline of the discovery and theory.

The uncertainty principle translates to these fluctuations in that we can only know the probability of finding a quantum fluctuation in a certain location or with a certain amplitude.

We could just call them fluctuations, but the term "quantum fluctuations" is more accurate because the fluctuations are rooted in the probabilistic nature of quantum mechanics; the discrete properties of quantum mechanics: energy, spin, position and momentum, that give rise to quantum fluctuations because they allow for the possibility of random fluctuations in the energy density of space-time, measurable as the average energy of the photons; their temperature.

We might say that the stock market is fluctuating, or that the weather is fluctuating, but saying "quantum fluctuations" helps distinguish these fluctuations.

Also, the term "quantum fluctuations" has a long history in physics. It was first used by Paul Dirac in the 1920s to describe random fluctuations in the energy density of the vacuum. Since then, the term has been used to describe a wide variety of quantum phenomena, including the fluctuations that are thought to have given rise to the observable CMB features.

If the universe had not undergone inflation, then these probabilistic fluctuations would have remained very small. However, during inflation, the universe expanded very rapidly, causing the quantum fluctuations to be baked in.

It is possible that there is another physical mechanism that we don't yet understand, that could produce such fluctuations, but until we find it, quantum fluctuations remain the best explanation.

There are discrete acoustic peaks in the CMB that were caused by the gravitational collapse of perturbations that were seeded by quantum fluctuations. These perturbations grew into classical acoustic waves, which then interfered with each other to form the discrete peaks and troughs observed, so the discrete features directly visible in the CMB are not inherently quantum.

Now, finding something that is small enough that can be expanded big enough, may seem like a textbook case of confirmation bias. But that doesn't mean its wrong... it's just the most plausible theory most people can agree on.

As for deriving ℏ from the CMB, you would have to cancel out all other factors, so no, probably not without knowing the details of inflation.

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    $\begingroup$ " it's just the most plausible theory most people can agree on." I agree, the field is open for research considering also that gravity has not been definitively quantized. $\endgroup$
    – anna v
    Jun 20, 2023 at 6:10
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    $\begingroup$ "If the universe had not undergone inflation, then we would expect to see the CMB to be perfectly uniform." Disagreeing with this part, because without inflation the distant parts of the universe would not be thermally the same. I.e. they would be very different and thus we would see big differences in CMB. $\endgroup$
    – M.S.
    Jun 20, 2023 at 10:48
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    $\begingroup$ "If the universe had not undergone inflation, we would not expect to see a CMB" False, and I don't want to dig out 1970s cosmology books to prove CMB was expected before inflation really took off. $\endgroup$
    – Joshua
    Jun 20, 2023 at 17:29
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    $\begingroup$ It is crucial in this area of physics to realise that smoothness cannot be assumed as a starting-point, and there is no need for a "cause" of non-smoothness. The mystery is not that the universe has irregularities; the surprise is that the irregularities are so small at early times. $\endgroup$ Jun 20, 2023 at 22:04
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    $\begingroup$ The reason I'm picky about it is I disbelieved Relativity for a long time because the physics fed me straw Newton as the thing to disprove rather than the fully advanced Newton's mechanics. $\endgroup$
    – Joshua
    Jun 20, 2023 at 23:14
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Here is a shorter, severely boiled-down answer:

There once was a time long ago when the effective size of the universe was so small that quantum mechanical effects (which occur on extremely tiny distance scales) dominated all of its dynamics.

This means that dynamical descriptions of the earliest moments in the history of the universe must include all the details of quantum physics that we know about.

Inflation then acted as the magnifying glass that blew up the imprint of those effects to cosmological distance scales.

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First of all, what we see e.g. in CMB is not quantum fluctuations per se. These are temperature fluctuations (or density fluctuations and so on) of quantum origin.

What it means is that in the beginning, they were quantum (vacuum) fluctuations of harmonic oscillator (inflaton field). If these fluctuations are always deep in the horizon, then the amplitude of these will decay as $ \propto 1/a(t)$ where $a(t)$ is the scale factor. However, as the Universe inflates, the fluctuations will eventually exit horizon and the amplitude of these fluctuations freezes in. Then these fluctuations get converted into curvature fluctuations and they leave imprints in CMB and provides the seed for structure formation. These fluctuations have ceased to be quantum at some point and therefore, I am not positive that you can measure $\hbar$ with it.

One may ask him/herself, why can't the inflaton field has other kind of fluctuations, for example it fluctuates in space(time). Indeed, if the aim of inflation is to isotropize and homogenize the Universe,then it seems contrived to require special initial conditions (that is no anisotropies and homogeneities) for inflation to start. Although it is quite model-dependent and IMO not completely settled, (a lot) of models seem to be stable against initial anisotropies and homogeneities. Thus, one often use the word "attractor".

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