How does the graph of V(φ) support the concept of slow-roll inflation?

In summary, the screenshot from Susskind's cosmology lecture shows a graph of V(φ) which demonstrates a gradual decline followed by a rapid decline. Inflation erases information before it happens, but leaves its own imprint on the resulting universe. The current best-fit for inflation is a potential given by V(φ) = αφ^2, which resembles a harmonic potential near its minimum. While the oscillating inflaton behaves like regular matter and can decay into standard model particles, the end of inflation is never instantaneous due to the slow roll conditions.
  • #1
robertjford80
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This is a screenshot from one of susskind's cosmology lectures.

Screenshot2012-06-18at90105PM.png


it shows a graph of V(φ). As you can see it slowly rules down then, bam, it rolls really fast down hill. I thought inflation erased all the information before it happened. So how does he know there is a gradual decline before a fast decline?
 
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  • #2
robertjford80 said:
This is a screenshot from one of susskind's cosmology lectures.

Screenshot2012-06-18at90105PM.png


it shows a graph of V(φ). As you can see it slowly rules down then, bam, it rolls really fast down hill. I thought inflation erased all the information before it happened. So how does he know there is a gradual decline before a fast decline?
Well, yes, inflation erases pretty much all information from before, but leaves its own imprint upon the resulting universe. That said, this is just a heuristic model of inflation used to explain the key concepts. There are many others. The current best-fit actually seems to be simply a potential given by:

[tex]V(\phi) = \alpha \phi^2[/tex].

Here [itex]\alpha[/itex] is a constant that gives the overall scale of the potential. This shouldn't be too much of a surprise since most any potential will look like a harmonic potential near its minimum, and it is pretty much only the behavior of the potential near the end of inflation that is detectable. So even if we had a complicated potential like the one shown in that graph, it might still come out just looking like a harmonic potential.
 
  • #3
Chalnoth said:
Well, yes, inflation erases pretty much all information from before, but leaves its own imprint upon the resulting universe. That said, this is just a heuristic model of inflation used to explain the key concepts. There are many others. The current best-fit actually seems to be simply a potential given by:

[tex]V(\phi) = \alpha \phi^2[/tex].

Here [itex]\alpha[/itex] is a constant that gives the overall scale of the potential. This shouldn't be too much of a surprise since most any potential will look like a harmonic potential near its minimum, and it is pretty much only the behavior of the potential near the end of inflation that is detectable. So even if we had a complicated potential like the one shown in that graph, it might still come out just looking like a harmonic potential.

I don't think that's true -- although I'm not an expert in inflation so please educate me if I'm wrong. But in the usual models, doesn't inflation end right away when the slow roll conditions are broken? In a potential like that, after you start oscillating in the minimum, the slow roll conditions do not hold so the universe is no longer inflating. In fact, I seem to remember that the oscillating inflaton behaves like regular matter, satisfying [itex] \rho \sim a^{-3} [/itex]. If the oscillating inflaton is coupled to regular standard model particles, then it can decay into them, heating up the universe and starting the regular big bang expansion.
 
  • #4
clamtrox said:
I don't think that's true -- although I'm not an expert in inflation so please educate me if I'm wrong. But in the usual models, doesn't inflation end right away when the slow roll conditions are broken? In a potential like that, after you start oscillating in the minimum, the slow roll conditions do not hold so the universe is no longer inflating. In fact, I seem to remember that the oscillating inflaton behaves like regular matter, satisfying [itex] \rho \sim a^{-3} [/itex]. If the oscillating inflaton is coupled to regular standard model particles, then it can decay into them, heating up the universe and starting the regular big bang expansion.
Right, but that end is never instantaneous, in any inflation model. The slow roll conditions are, after all, a statement that the change in the field value is very slow compared to the expansion. Such conditions cannot be broken instantaneously, because they involve one continuous value becoming significant in size compared to another. So inflation always has an at least somewhat gradual end.

I believe in realistic inflation models the end of inflation has to be fairly rapid, but it is never instantaneous.
 
  • #5


The graph of V(φ) represents the potential energy of the universe as a function of the scalar field φ. This is a key concept in the inflationary model of the universe, which suggests that the early universe underwent a rapid expansion driven by a scalar field. The gradual decline in the potential energy before the steep drop is known as "slow-roll" inflation, where the scalar field slowly decreases in value over time. This is supported by observational evidence, such as the cosmic microwave background radiation, which shows a nearly uniform distribution of matter on large scales, indicating a period of rapid expansion. While the exact details of the inflationary period are still being studied, the concept of slow-roll inflation is a well-established component of modern cosmology.
 

1. What is the expansion of the universe?

The expansion of the universe refers to the continuous increase in the distance between all galaxies and other celestial objects. This phenomenon was first observed by astronomer Edwin Hubble in the 1920s.

2. How does the expansion of the universe occur?

The expansion of the universe is believed to be caused by a force called dark energy, which is thought to make up about 70% of the total energy in the universe. This force acts against the gravitational pull of matter, causing the universe to expand at an accelerating rate.

3. Is the expansion of the universe constant?

No, the expansion of the universe is not constant. It was initially thought to be slowing down due to the gravitational pull of matter, but in the late 1990s, it was discovered that the expansion is actually accelerating. This means that the rate of expansion is increasing over time.

4. How is the expansion of the universe measured?

The expansion of the universe is measured using a unit called the Hubble constant, which represents the rate at which the universe is expanding. This constant is determined by measuring the redshift of light from distant galaxies, which is caused by the stretching of space as the light travels towards us.

5. Will the expansion of the universe continue forever?

It is currently believed that the expansion of the universe will continue forever. This is because dark energy is thought to be a constant force that will continue to push galaxies and other celestial objects further apart. However, this is still a topic of ongoing research and could change as we learn more about the universe.

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