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Featured Insights A Poor Man's CMB Primer. Part 5: Quantum Seeds - Comments

  1. Jul 26, 2017 #1

    bapowell

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  2. jcsd
  3. Jul 27, 2017 #2
    The "A Poor Man's CMB Primer" series has really been a treasure at PF! Thanks!
     
  4. Aug 3, 2017 #3
    Just read it, nice. You bring it to where it "all boils down to"! Excellent work.
     
  5. Dec 20, 2017 #4

    Urs Schreiber

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    @bapowell You speak of quantum fluctuations and their decoherence, and that seems very plausible. But just from the formulas that you discuss, is it clear that ##\delta\phi_k## needs to have a quantum origin?

    It looks, superficially, like all derivations that you sketch in the entry would remain valid if we think of ##\delta \phi_k## as some classical stochastic contribution. What is it that allows us to deduce that the CMB fluctuations seen are of quantum origin, as opposed to some classical stochastic perturbations?

    I suppose it must be that we can somehow estimate the total effect of quantum fluctuations from first principles and then find that this exhausts the seen CMB fluctuations?
     
  6. Dec 22, 2017 #5
    Excellent article Bapowell, I particularly liked how you detailed the scalar field equation of state with regards to inflation.
     
  7. Dec 22, 2017 #6
    Yes there is correlations in those formulas to QFT. However thats a lengthy topic unto itself. The potential and kinetic energy relations are very similar to the equation of state formula Bapowell posted.
     
  8. Dec 22, 2017 #7

    Urs Schreiber

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    Thanks for offering a reply. It remains a bit mysterious to me what you have in mind. Maybe you can point me to the relevant page in some textbook or review? Thanks!
     
  9. Dec 22, 2017 #8
    see the section detailing to equations 16 to 18

    https://arxiv.org/pdf/hep-ph/0503268.pdf

    as one example of its application, I've seen other references prior but can't recal which one offhand so this was a quick search. I'll see if I can relocate the one I read some time back that applied directly to the scalar field equation of state equation posted in the insight article.

    Here is the Klien Gordon relations to the [tex]P=-\rho[/tex]
    https://rd.springer.com/article/10.1007/BF00650285?no-access=true
     
    Last edited: Dec 22, 2017
  10. Dec 22, 2017 #9

    Urs Schreiber

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    Thanks for offering pointers. But please allow me to recall that the question I am asking is how exactly one deduces that the CMB fluctuations originate in quantum fluctuations, as opposed to some generic stochastic perturbance of other or unknown origin. (I have no reason to doubt that it's quantum fluctuations, but I realize that I don't know what the precise evidence is, so I thought I'd check.)

    I gather one criterion is that quantum fluctuations are mostly Gaussian distributed and also the CMB fluctuations are mostly Gaussian distributed, so that this is consistent with assuming quantum origin of the fluctuations.

    I am opening now
    On p. 85, in the intro of chapter 6, they state the claim whose evidence I am asking for, where they say:

    "we will see that in the inflationary cosmology the randomness of cosmological perturbations does have its origin in quantum uncertainty."

    I need to keep reading to see where in the book this "we will see" is happening. Maybe it's equation (24.51). Unfortunately I don't have time to dig around more right now. Will try to come back to this later.
     
  11. Dec 22, 2017 #10
    Ah ok I didn't catch the meaning of your question.
    Anyways the relations I posted in those articles are related to inflationary models involving the inflaton.

    See equations 2.1 onward

    Encyclopedia Inflationaris

    https://arxiv.org/abs/1303.3787

    2.1 The slow-roll phase
    "Let us consider a single-field inflationary model with a minimal kinetic term and a potential V (φ). The behavior of the system is controlled by the Friedmann-Lemaıtre and Klein-Gordon
    equations, namely" then it goes into the equations which copy paste doesn't handle well.

    Page 16

    It will step into Fourier space further on via the Muhkanov Sasaki variable of the 4th order fluctuations.
     
    Last edited: Dec 22, 2017
  12. Dec 24, 2017 #11

    bapowell

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    Hi @Urs Schreiber. Sorry for the delayed response. As far as I know, there's nothing about the CMB anisotropies that singles out a quantum mechanical origin. Just before I got into the field in 2003 or so, the competing theory of structure formation (and, hence, CMB anisotropy) arose out of perturbations generated from cosmic strings. If I recall correctly, WMAP nailed that coffin; specifically, it was the adiabaticity of the perturbations (that all fluid components are perturbed by the same amount relative to their background densities) that could not be accounted for with cosmic strings.

    It would seem that a key aspect here is that the perturbations begin in the adiabatic vacuum of the spacetime (during inflation, the vacuum is taken to be that of free falling observers), and that their statistics are Gaussian. (Of course, non-Gaussian fluctuations can still be handled by inflation, by adding non-canonical or non-slow roll dynamics).

    It's a good question: I don't have a complete answer!
     
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