Eternal Inflation.

[Bill S]

I’m trying to grasp, in a non-technical way, the ideas underlying the theory of eternal inflation. If I post some of my thoughts, I would really welcome comments/criticism as I go.

 

In order to have a situation in which this eternal inflation can operate, we must have an infinite vacuum, with a measurable vacuum energy. Quantum mechanics provides us with this, because it forbids us from having the classical vacuum, which can be identified as absolutely nothing.

 

Absolute nothing provides absolute information about its state, and the uncertainty principle does not give us that luxury. There has to be the possibility that the vacuum is something. In fact, to the best of our knowledge, the vacuum is, on the scale of the Planck’s length, a very active and energetic place.

[mathematic]

 

 

In order to have a situation in which this eternal inflation can operate, we must have an infinite vacuum, with a measurable vacuum energy.

 

Do you have any reference for this statement?

[MigL]

I don't know about an infinite ( in extent ? ) vacuum. but a non-zero vacuum energy is a requirement for quantum fluctuations.

( as well as a requirement for QM in general )

That would give the initial conditions, but at some point, pressure conditions have to favor inflation for expansion to take off.

Otherwise the fluctuation just 'settles' again.

And there are countless quantum fluctuations occurring all around you. I think you'd notice if a new universe started expanding in your pocket.

[Bill S]

Do you have any reference for this statement?

 

 

I’ve just read Alex Vilenkin’s “Many Worlds in One”. There were several references which gave me this impression.

 

 

I don't know about an infinite ( in extent ? ) vacuum. but a non-zero vacuum energy is a requirement for quantum fluctuations.

 

Possibly “eternal” would have been a better word. Infinite extent (in space) seems to be optional, but infinite extent into past and future appear to be an essential feature of “eternal” inflation.

Given this eternally existing vacuum; my next impression is that the variations in vacuum energy can be visualised as a “landscape” in which higher energy conditions are represented by hills and lower by valleys. The lowest of these valleys would be the “true vacuum”, and the hills and slopes represent “false vacuum” states, which are unstable.

[Bill S]

Images of this landscape are inhabited by scalar fields; represented by spheres. These spheres appear to have energy levels that reflect the energy level of their positions in relation to the height they occupy on the landscape.

 

A scalar field that is at, or near, the top of a hill will equate to a false vacuum state.

 

If/when a sphere rolls down to a lower energy level its energy dissipates as a “big bang”, and results in the formation of a new universe.

[MigL]

Not quite.

Hold a pencil at arm's length. that pencil has a definite potential energy.

now drop it so it lands on its sharp end ( not realistic, I know ). The pencil is now at a 'false zero' energy level, but it has rotational symmetry.

Now the pencil falls over on its side in a preferred direction, breaking the symmetry. The pencil is now at true zero energy.

 

It is the symmetry break which provides the impetus for the resultant inflation ( not Big Bang ). First book I read in the topic was Alan Guth's, the idea's originator.

Vacuum energy, and its false and real values, has proven extremely difficult to get a handle on.

[Bill S]

I didn’t intend giving the impression |I thought the “big bang” caused the inflation; rather, I saw it as a result. Is it better to consider the image of a sphere rolling down a slope as a visual representation of a symmetry break?

Vilenkin talks of a situation in which a false vacuum exists at every point in space. This is represented by a sphere resting in a valley that is at a higher level than the true vacuum. Would that equate to your pencil balanced on its point?