Quantum fluctuations during inflation

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some_dude
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Quantum fluctuations during inflation

Postby some_dude » Fri Jan 17, 2014 11:43 am UTC

The density perturbations that we see in the CMB and later became galaxies are thought to have originated as quantum fluctuations in the inflaton field that were amplified to the macro scale by inflation and turned into density perturbations of matter and radiation during reheating at the end of inflation where the inflaton field decayed to other particles. That all sounds nice but thinking about it I ran into a couple of issues that didn't make sense to me:

1. I can see how the radius of a fluctuation grows during inflation, but how does its depth grow? That it gets strecthed out seems pretty useless if the energy density contrast between the perturbation and the average is still close to zero.
2. How do the quantum flucatuations become permanent? There must be some mechanism transferring energy from the inflaton field to the fluctuations to "promote" them to real perturbations. I can imagine that inflation heuristically can be said to separate virtual particle-antiparticle pairs before they can annihilate thus making them into real particles, but that would probably be to take the virtual particle heuristic too literally.

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Re: Quantum fluctuations during inflation

Postby doogly » Fri Jan 17, 2014 8:39 pm UTC

"Quantum" doesn't mean fake. You don't need to get "promoted" to realness.

You do need to get bigger though, and that is what gravity does! If things are uniform, gravity pulls in all directions equally, and nothing goes anywhere. Fluctuate to a little more density over in this area. Now it also pulls on its neighbors more, and so on. Since the universe is also expanding you don't wind up with a single huge black hole, but that is where the extra kick comes from.
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Re: Quantum fluctuations during inflation

Postby some_dude » Sat Jan 18, 2014 12:05 am UTC

But gravity is utterly overpowered by the (quasi-)exponential expansion during inflation, I don't see how gravity would amplify the depth of the fluctuations in any significant way.

Also I probably worded myself poorly talking about the "virtualness" or "realness" of the fluctuations, but what I'm trying to get at is that normally quantum fluctuations annihilate on a very short time-scale so how do the quantum fluctuations in the inflaton field manage to survive?
EDIT: Just realized that inflation only lasts about 10-33 seconds so I guess some of the quantum fluctuations just don't have enough time to annihilate before decaying into other particles during reheating.

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Re: Quantum fluctuations during inflation

Postby lgw » Sat Jan 18, 2014 12:53 am UTC

I'll take a stab at this - at least it will give Doogly more text to correct. :lol: The universe very early on was nearly perfectly uniform, but because of quantum fluctuations some small variation in energy density had to exist. Inflation blew this up to every-so-slighty denser and less-dense pockets that would eventually become clusters of galaxies IIRC, or something much larger than galaxies.

The universe spent a long time - almost 400k years - as a plasma where the dominant forces were gravity and light pressure, as electrons weren't coupled to protons in any stable way yet. (I believe that's a "relativistic plasma", but the term might be more specific.) This was enough time, relative to the size of these pockets, for gravity to significantly exaggerate the density differences. The slightly denser areas would accumulate matter gradually from the slightly-less-dense areas. Without that light pressure resisting increased density, the differences between the more- and less-dense regions would have been far greater, and the universe would be a very different place. But as it was the dense pockets would "bounce" in simple harmonic motion, as light pressure would increase with density.

When the universe cooled to where atoms were stable and the light pressure went away, denser clumps within each denser pocket would gradually collect nearby matter and fall together to form galaxies (instead of being bounced by light pressure).
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Re: Quantum fluctuations during inflation

Postby doogly » Sat Jan 18, 2014 2:38 am UTC

At the end of inflation, what you have is a now very very large uniform that is almost perfectly homogenous and isotropic. Much more so than it could ever be without something like inflation, as distant regions (more than hubble length away) are not in causal contact with each other anymore.

But, it's not exactly perfect. There are some inhomogeneities due to the quantum fluctuations of the inflaton field. That is the status at the end of inflation. Gravitational instability acting from end of inflation onward is what gets you to galaxies and such.

I recommend Mukhanov's book, Physical Foundations of Cosmology.

This is pretty much what was suggested above, I think. I have a headache though, so if this is stuff you already know and not getting at the question you are actually asking, poke more.
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Re: Quantum fluctuations during inflation

Postby some_dude » Sun Jan 19, 2014 1:49 am UTC

I'm aware of how the perturbations generally evolve after inflation. What I'm trying to get at, to be more specific, is that some mechanism that can greatly increase the amplitude of the fluctuations in addition to the size seems needed since the largest density contrasts inferred from the CMB are dρ/ρ ~ 10-2 which is small but huge compared to what I'd expect from some quantum fluctuation which has only had ~300000 years to evolve with most of that time being in the radiation dominated epoch where density perturbations grow only logarithmically. I've been skimming over some of Kolb & Turner's The Early Universe (which is a bit above my level) and I can kind of see how tiny fluctuations in the inflaton field might translate to larger differences in the density from their equation 8.51:
(dρ/ρ)horizon ≈ H2/(dφ/dt)
where φ is the inflaton scalar field and H is the Hubble parameter. I'm not sure how to interpret this though, Kolb & Turner is nice but not the most readable textbook (and Ryden's Introduction to Cosmology which is otherwise great and very readable doesn't discuss this) so I'd just like an explanation of this and whether the Kolb & Turner equation is actually the answer.

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Re: Quantum fluctuations during inflation

Postby lgw » Mon Jan 20, 2014 6:00 pm UTC

300k years sounds like quite a lot of time, to me, relative to the size (at the time) of these density variations. If gravity - light pressure gave a net billionth of a g acceleration to atoms in the less dense areas, that would be more than enough.
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Re: Quantum fluctuations during inflation

Postby gmalivuk » Thu Jan 23, 2014 11:06 pm UTC

some_dude wrote:some mechanism that can greatly increase the amplitude of the fluctuations in addition to the size seems needed
Why can't gravity be that mechanism?
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Re: Quantum fluctuations during inflation

Postby some_dude » Sat Jan 25, 2014 2:49 pm UTC

gmalivuk wrote:
some_dude wrote:some mechanism that can greatly increase the amplitude of the fluctuations in addition to the size seems needed
Why can't gravity be that mechanism?


Gravity is what made the perturbations observed in the CMB of amplitude dρ/ρ ~ 10-5 (not 10-2 as I wrote previously) grow into galaxy clusters, but what I'm trying to get at is what amplified them from tiny quantum fluctuations to 10-5 in the first place? Gravity alone couldn't have done that in just 250000 years (the first ~50000 years after inflation the universe was radiation dominated and density perturbations only grew logarithmically with time i.e. hardly at all, after that they grew as t2/3 rather than exponentially as expansion slowed down the growth).

Anyway I can see that the math checks out:
dρ/ρ ~ dφ (dV/dφ)/V where V is the potential of the inflaton field.
Where dφ = H/(2pi) is the amplitude of quantum fluctuations in the inflaton field during inflation. Using a potential of the form V(φ)=mφn where m is the mass of the inflaton you can get dρ/ρ ~ 10-5 for realistic m.

My question then becomes why were the initial quantum fluctuations of amplitude dφ = H/(2pi), but I probably don't have the required amount of knowledge of QFT to understand the answer to that one.

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Re: Quantum fluctuations during inflation

Postby Garganzuul » Mon Feb 03, 2014 6:47 am UTC

Great topic.

I'll bet on entire galaxies appearing and disappearing at the edge of space, and that this is where the most energetic cosmic rays come from. :mrgreen:


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