How did the quantum fluctuations in the inflationary universe turned classical?

[chronnox]

Im trying to understand inflation, specially the part of structure formation, so I am following Mukhanov's Book. There he does an analysis on quantum fluctuations, more specifically he quantize the Newtonian potential and finds the power spectrum and turns out to be scale invariant. I kind of understand that, but what i don't understand at all is how this supossedly quantum fluctuation of the FRW metric turned classical and gave birth to all the inhomogenities and anisotropies in our universe. Can anyone help me on this

 

[George Jones]

Im trying to understand inflation, specially the part of structure formation, so I am following Mukhanov's Book. There he does an analysis on quantum fluctuations, more specifically he quantize the Newtonian potential and finds the power spectrum and turns out to be scale invariant. I kind of understand that, but what i don't understand at all is how this supossedly quantum fluctuation of the FRW metric turned classical and gave birth to all the inhomogenities and anisotropies in our universe. Can anyone help me on this

This a question that I find fascinating. Viatcheslav Mukhanov, Steven Weinberg, and Roger Penrose all agree that this is an example of the measurement problem in standard quantum mechanics. Both Mukhanov and Weinberg believe that decoherence plays plays a role, and that decherence (as we now understand it) alone is not sufficient.

As I understand things, the state (pun intended) of the measurement problem in quantum mechanice is roughly this. Decoherence takes us from a quantum superposition to a mixture of classical states, but does not (yet) show in general how to pick out one of the classical states.

Mukhanov believes that, in this cosmological context, the measurement problem forces us into the many-worlds interpretation of quantum mechanics. From pages 348, 349 of Physical Foundations of Cosmology by Mukhanov:

How do quantum fluctuations become classical? ... Decoherence is a necessary condition for the emergence of classical inhomogeneities and can easily be justified for amplified cosmological perturbations. However, decoherence is not sufficient ... It can be shown that as a result of unitary evolution we obtain a state which is a superposition of many macroscopically different states, each corresponding to a particular realization of galaxy distribution. Many of these realizations have the same statistical properties. ... Therefore, to pick an observed macroscopic state from the superposition we have to appeal either to Bohr's reduction postulate or to Everett's many-worlds interpretation of quantum mechanics. The first possibility does not look convincing in the cosmological context.

For Weinberg, this is no more or less puzzling than getting a classical output from our apparatus when we measure the quantum mechanical spin of a particle. From page 476 of the new book, Cosmology, by Weinberg:

These are quantum averages, not averages over an ensemble of classical field configurations. ... Just as in the measurement of a spin in the laboratory, some sort of decoherence must set in; the field configurations must become locked into one of an ensemble of classical configurations, ... It is not apparent just how this happens, ...

Penrose points out that a quantum superposition of field configurations corresponds to a quantum superposition of spacetime geometries, since different field configurations have different stress-energy tensors, and thus correspond to different solutions of Einstein's equation. From page 862 (hardcover edition) of The Road to Reality by Penrose (U = unitary,; R = reduction)

How then is this FLRW-symmetric vast quantum superposition of irregular geometries supposed to give rise to something resembling one specific 'almost FLRW-symmetric' universe which is perturbed only in some very minor way that is consistent with observation? It should be clear to the reader that there is no way that this can happen entirely within the U-evolution of standard quantum mechanics, ... There must be something of the nature of an R-process taking place, ... The key is that irregularities arising from 'quantum fluctuations' cannot come about without some R-like action, whereby the the single initial quantum state somehow resolves itself into a probability mixture of different states. This takes us back to the issues addressed in Chapter 29, where different attitudes to the 'reality' of R were discussed.

As I said, fascinating stuff!

 

[chronnox]

Thanks for your reply, but now i have more questions

For Weinberg, this is no more or less puzzling than getting a classical output from our apparatus when we measure the quantum mechanical spin of a particle.

This is exactly where i am confused, as far as i know, when we measure the quantum mechanical spin of a particle, we need a time of measurement, a basis, and a measuring device. In the cosmological context i don't see these, so my questions are:

1) What is performing the measurement?
2) Precisely, what is the set of quantum observables that is being measured? and what determines them?
3) When is this measurement taking place?

In the case of the quantum mechanical spin of a particle i can answer this with a Stern-Gerlach type experiment, but in the cosmological scenario i don't see this. The Many-World interpretation to me seems to be in one on one correspondence with these issues. (time of measurement, basis, measuring device).

I still have more questions, specially with decoherence but i think these are the ones which confuses me the most. Thanks again for your help.