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

[bapowell]

bapowell submitted a new PF Insights post

A Poor Man's CMB Primer. Part 5: Quantum Seeds

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

The "A Poor Man's CMB Primer" series has really been a treasure at PF! Thanks!

 

[jerromyjon]

Just read it, nice. You bring it to where it "all boils down to"! Excellent work.

 

[Urs Schreiber]

@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?

 

[Mordred]

Excellent article Bapowell, I particularly liked how you detailed the scalar field equation of state with regards to inflation.

 

[Mordred]

@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?

Yes there is correlations in those formulas to QFT. However that's a lengthy topic unto itself. The potential and kinetic energy relations are very similar to the equation of state formula Bapowell posted.

 

[Urs Schreiber]

Yes there is correlations in those formulas to QFT. However that's a lengthy topic unto itself. The potential and kinetic energy relations are very similar to the equation of state formula Bapowell posted.

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!

 

[Mordred]

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 $$P=-\rho$$
https://rd.springer.com/article/10.1007/BF00650285?no-access=true

 

[Urs Schreiber]

see...

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

• D. Lyth, A. Liddle, "The primordial density perturbation -- Cosmology, Inflation and the Origin of Structure", Cambridge 2009

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.

 

[Mordred]

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.

 

[bapowell]

Hi @[URL='https://www.physicsforums.com/insights/author/urs-schreiber/']Urs Schreiber[/URL]. 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!