Understanding inflationary cosmology

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In summary, according to the authors of this paper, modes of a given wavelength will "freeze out" upon first crossing the Hubble radius during inflation, remain (nearly) constant in amplitude while longer than the Hubble radius, and then resume oscillation upon reentering the Hubble radius. The Temporal Oscillations of Modes with Nearby Wavelengths are Coherent, Giving Rise to a Sharp Pattern of Peaks and Troughs in the Cosmic Microwave Background Power Spectrum. Not understanding it either.
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windy miller
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There is a prediction I have often hear about regarding inflationary cosmology but I am having trouble grasping what it really means. I am wondering if anyone could give a layman explanation fo the following :
https://arxiv.org/pdf/1312.7619.pdf
"Modes of a given (comoving) wavelength should “freeze out” upon first crossing the Hubble radius during inflation, remain (nearly) constant in amplitude while longer than the Hubble radius, and then resume oscillation upon reentering the Hubble radius. The tem- poral oscillations of modes with nearby wavelengths are therefore coherent [10], giving rise to a sharp pattern of peaks and troughs in the cosmic microwave background (CMB) power spectrum.
 
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windy miller said:
"Modes of a given (comoving) wavelength should “freeze out” upon first crossing the Hubble radius during inflation, remain (nearly) constant in amplitude while longer than the Hubble radius, and then resume oscillation upon reentering the Hubble radius. The tem- poral oscillations of modes with nearby wavelengths are therefore coherent [10], giving rise to a sharp pattern of peaks and troughs in the cosmic microwave background (CMB) power spectrum.

First, this is really an "A" level topic, not an "I" level topic. This is to be expected with most aspects of inflationary cosmology. I'll try to give a brief "I" level answer here, and then give a reference (which is most definitely an "A" level reference) that goes into more detail. I emphasize that this description is heuristic and will leave a lot of loose ends; that's unavoidable.

The "modes" being referred to are quantum fluctuations in the spacetime curvature of the universe during inflation. Classically, the curvature is constant on any spacelike surface of constant FRW coordinate time; but once we bring in QM we have to pay attention to the uncertainty principle, which in this context says that the spacetime curvature can't be exactly a single value everywhere. There will be unavoidable fluctuations. These fluctuations will occur with widely varying wavelengths, and as inflation proceeds those wavelengths will be "stretched" by enormous amounts because of the rapidly accelerating expansion of the universe.

Once a fluctuation's wavelength is stretched so much that it becomes longer than the Hubble radius, one end of the wave can no longer causally communicate with the other end. That means the amplitude of the wave--its deviation from the "average" value of spacetime curvature--becomes "frozen": it stops fluctuating (which it had been doing up until that point--that is what "quantum fluctuations of spacetime curvature" means). Explaining in more detail why this happens is beyond the scope of an "I" level discussion, and also beyond my expertise; all I can do is describe what happens in the phenomenon referred to.

At some point after inflation ends, the Hubble radius will have increased to the point where it becomes larger than the wavelength of the "frozen" wave. At that point, the two ends of the wave can causally communicate with each other again. However, conditions in the universe are now very different: instead of all the energy density (which is what drives the average spacetime curvature) being contained in the "false vacuum" state of the inflaton field, it is now contained in the hot, dense, rapidly expanding matter and radiation that fills the universe. That drastically changes the dynamics of the wave: its amplitude, while it will not remain exactly fixed (briefly, overdense regions will become more overdense, so waves with amplitudes over the average curvature will have their amplitudes increase; underdense regions, waves with amplitudes under the average curvature, will do the opposite), will fluctuate, if at all, by only a very small amount. So the overall pattern of fluctuations over the universe will be basically the same as the pattern at the end of inflation (the time evolution just described is easy to run in reverse, so we can evolve the pattern we observe today back to the pattern at CMB formation, and from there the amplitudes stay constant back to the end of inflation), which means it carries information about the quantum fluctuations that took place during inflation (and therefore about the inflation process itself).

At some point further on, the CMB is formed, and the pattern of spacetime curvature fluctuations described above leaves an "imprint" of a similar pattern of fluctuations in the CMB radiation. Which we, in turn, observe billions of years later with the Planck satellite.

The following reference (reference 10 in the Guth et al. paper linked to in the OP) is a better one for understanding the specific phenomenon described above:

https://arxiv.org/abs/hep-ph/0309057

See in particular Fig. 2 and the discussion surrounding it.
 
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Thanks Peter that is very helpful, really appreciate you taking the time to explain it.
 
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windy miller said:
Thanks Peter

You're welcome!
 

1. What is inflationary cosmology?

Inflationary cosmology is a theory in modern cosmology that explains the rapid expansion of the universe in its early stages. It proposes that the universe underwent a period of exponential expansion in the first fraction of a second after the Big Bang.

2. What evidence supports inflationary cosmology?

One of the main pieces of evidence for inflationary cosmology is the observation of the cosmic microwave background radiation. This radiation is a remnant of the Big Bang and shows patterns that align with predictions made by inflationary cosmology. Additionally, the theory also explains the observed homogeneity and flatness of the universe.

3. How does inflationary cosmology solve the horizon problem?

The horizon problem is the discrepancy between the observed uniformity of the universe and the fact that different regions of the universe are not causally connected. Inflationary cosmology solves this problem by proposing that during the period of rapid expansion, all regions of the universe were in close proximity and therefore could have reached a state of thermal equilibrium.

4. What is the role of the inflaton field in inflationary cosmology?

The inflaton field is a hypothetical scalar field that is responsible for driving the rapid expansion of the universe during inflation. It is thought to have decayed after inflation ended, releasing energy and particles that eventually formed the matter and energy in the universe today.

5. Are there any alternative theories to inflationary cosmology?

Yes, there are alternative theories to inflationary cosmology, such as the cyclic model and the ekpyrotic model. These theories propose different mechanisms for the early expansion of the universe and have their own unique predictions and challenges. However, inflationary cosmology remains the most widely accepted theory due to its ability to explain many observed phenomena and its consistency with current data.

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