# Inflation & Pertubative 1st order Cosmology: A timeline?

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1. Jun 5, 2015

### JJNic

Hey there,
i have a question regarding basic inflation and structure formation via linear first order perturbation theory in cosmology.

I read through different material (Baumann lecture notes, wikipedia articles, Mukhanov, ...), but at this point i am just confused and find it hard to get an overall picture.

My basic questions are: What happened when? When were the perturbations created? when did they leave the horizon and when did they reenter the horizon? On the other hand, i feel like i am still missing a lot more.

Out of my head, the thing would look like this (its not even a timeline, just a order):
1) Big Bang Singularity
2) Oscillating primordial quantum fluctuations
3) Inflation Starts
4) Fluctuations get stretched to the size of the observable universe (thereby creating homogeneity?)
5) Fluctuations leave horizon and freeze
6) Inflation Ends
8) Fluctuations reenter horizon (and destroy homogeneity?) and create large scale structure of the universe
9) Photon Decoupling/CMB
10) Matter Dominated phase
11) Dark Matter Dominated phase

...But, i dont feel like i fully understand it nor do i know if its right or wrong. Like, the perturbations have to reenter before the Photon decoupling, because otherwise they would not be visible in the CMB spectrum, right?
Wouldnt they start to oscillate again once theyre back in the horizon? What effect would that have?

It would be very nice if any of you could help me get the picture right :)

Thanks!

PS: Sorry, at first i created this thread in the GR section yesterday, but now just realized theres actually a Cosmology section as well.

2. Jun 5, 2015

### Chalnoth

The perturbations stem from quantum fluctuations in the inflaton field while inflation was ongoing. Due to the rate of inflation, each perturbation leaves the horizon almost immediately after it forms. The perturbations re-enter the horizon at a time determined by when they originally left it.

The basic picture here is that you have a wave of some (rather short) wavelength created during inflation, which is an inevitable result of quantum mechanics. This wave rapidly grows so that its wavelength is much larger than the horizon, and so for the most part it gets "frozen" (in the sense that the wave doesn't oscillate), though it continues to expand as the universe expands. As the expansion slows later on, when the horizon becomes comparable in size to the wavelength, the wave is allowed to start oscillating again.

1) Nope. There was no singularity. The singularity is a fiction in the math that is an indication that our theories are incomplete.
2) This occurred during inflation, not before. Inflation wipes out everything that happens before.
4) They don't get stretched uniformly. They get stretched depending upon when they were initially formed, and how much the universe has expanded since that time.
8) No, fluctuations don't destroy homogeneity. Homogeneity is approximate. The fluctuations just start to oscillate again (they're basically sound waves). These primordial sound waves act as seeds for structure formation, as the attractive nature of gravity draws the more dense regions together into clumps.
10) The matter dominated phase starts long before the CMB is emitted. During the radiation dominated era, matter like protons and electrons behave like radiation (i.e., they have kinetic energy significantly above their rest mass energy). The CMB isn't emitted until the hydrogen/helium plasma cools to a gas, which occurs long after the protons and electrons have become non-relativistic.
11) The ratio of dark matter to matter is essentially unchanged since the radiation dominated phase ended.

3. Jun 8, 2015

### JJNic

Hey,

I see, so the quantum fluctuations are still reentering the horizon today since some of the modes that were created during inflation are so large that they just did not enter until recently?
What is meant by oscillating in terms of physics consequences though? I guess i realize its the opposite of freezing, but what does it lead to? That they move through space and start clumping up matter and therefore create the seeds for galaxies?

I also have a follow up question, that is not really related to the previous one, but made me think. Can one interpret the matter we have today as a kind of Hawking radiation created by inflation, the quantum fluctuations and the particle horizon of the universe? Like quantum fluctuations usually vanish (not per se of course, but in terms of actually creating mass) except for at (black hole) horizons and i guess thats called hawking radiation by definition. But to us the primordial quantum fluctuations created during inflation are pretty real.... so does that make sense?

Thanks,
Best

4. Jun 8, 2015

### bapowell

Yup.
When the perturbations re-enter the horizon during radiation-dominated expansion, they set up standing waves in the baryon-photon plasma. Perturbations in fluids that are decoupled from the baryon-photon plasma, like cold dark matter, however, do not oscillate; instead, they grow through instability. When the universe cools down to the point where the photons decouple from the plasma, the standing waves in the baryon-photon plasma cease (because there is not sufficient radiation pressure to support the standing waves); at this point, the baryons contribute to the growing dark matter perturbations. These are the seeds of structure formation.
The quantum fluctuations generated during inflation can be associated with a 'de Sitter' temperature associated with the event horizon of the de Sitter space, $T = H/2\pi$, which you might notice is the amplitude of the massless scalar perturbations.

Last edited: Jun 8, 2015
5. Jun 8, 2015

### Chalnoth

Early-on, they're simply sound waves. The more dense regions, however, instead of bouncing back as with sound waves in our own atmosphere, start to just fall inward. This is largely due to dark matter (which doesn't experience pressure like normal matter does when it's in a plasma state).

No.

The matter that's around today would have been created as a consequence of inflation ending: as the particle field that drove inflation decayed, it produced all of the particles that are around us.

The sound waves, however, those can be thought of as a result of Hawking radiation during inflation. So you've got this huge overall temperature (from the decay of the Inflaton), and tiny deviations from that temperature due to the quantum fluctuations. It's not exactly identical to Hawking radiation, but it's the same basic concept.