Why decaying false-vacuum necessary for inflation?

[Lapidus]

According to inflation theory, there first was a scalar quantum field in a false-vacuum (the inflaton). The whole inflationary expansion only got started when the inflaton decayed to its true vacuum.

But then people say that the dark energy that causes the universe to expand today, could be just a constant scalar field without any decaying.

My question: why had the inflaton to decay in order to inflate the universe? Why couldn't it be just a constant scalar quantum field, with high energy enough to make the universe expand (and decay afterwards)? What's the matter with a decaying false-vacuum?THANKS

 

[PeterDonis]

The whole inflationary expansion only got started when the inflaton decayed to its true vacuum.

No. The inflationary expansion stopped when the inflaton field decayed from false vacuum to true vacuum. As long as the inflaton was in the false vacuum state, inflation was happening.

 

[Lapidus]

Okay! Problem solved, I guess. Thank you!

 

[Lapidus]

But what do people mean when they say that "the rapid change was due to a phase change, leading to the introduction of energy into the universe with effect of antigravity...with the cooling of the universe, symmetry breaking occurred which had the effect of a phase change"?

In the pop-science books I read both. That what Peter Donis says agrees what I read in Greene "Hidden Reality", but Halpern "Edge of the Universe" says

"A surprisingly rapid expansion would require a special mechanism. Guth proposed an idea connected to supercooling. ...According to Guth’s inflationary scheme, the universe began in a state of high symmetry, called the false vacuum...Through the mechanism of spontaneous symmetry-breaking and the production of a scalar field, Guth saw the opportunity to describe a phase change for the primordial universe, analogous to supercooling...As the universe continued to cool, patches of false vacuum would spontaneously lose their initial symmetry, decay into a lower energy state, and produce a scalar field. The field—called an inflaton—would trigger a brief but explosive inflationary epoch.

(my emphasis)

 

[PeterDonis]

In the pop-science books I read both.

Pop science books are not good sources if you actually want to learn about the science.

For a quick look at a simple version of the physics behind inflation, check out Figure 10 in section 6.1 of this series of lectures (the series itself is worth reading):

http://arxiv.org/abs/0907.5424

Basically, the scalar field $\phi$ starts out on the flat area on the left. While it is there, it can drive inflation (because, as the text says, its potential energy exceeds its kinetic energy). However, since that area is not perfectly flat, the field will sooner or later start "rolling" to the right down the slope. The slope starts out gentle (this is the "slow roll" talked about in the text), but then grows steeper. When it gets steep enough, the scalar field can no longer drive inflation (actually this is a combination of increasing steepness and time spent rolling--the key criterion is that the field's kinetic energy now exceeds its potential energy), so inflation stops (this is the point marked $\phi_{end}$). The field $\phi$ then ends up in the trough marked "reheating"; once it's there, it can't get out, and its kinetic energy (from rolling down the slope) gets converted to ordinary matter and radiation (this is the "reheating"), which is expanding rapidly and starts the standard hot Big Bang process.

Of course, the model described above is not necessarily complete. In this model, the scalar field is always there, and the starting state in which it is up on the flat area on the left is called the "false vacuum" state. The "phase transition" is the process of the field rolling down the slope, which eventually stops inflation; there is no phase transition needed to start it, since it's already happening at the start of this model (when the field is up on the flat area on the left). The end state of the model, with the scalar field down in the trough, is called the "true vacuum" state. (This is how I was using those terms in my previous post.) But the model evidently does not address the question of how the scalar field got up on the flat area in the first place. Was it always there? Or did some previous process put it there?

I'm unable to find a good online source discussing the details of Guth's original model, but IIRC it did include a previous transition from a state he was calling "false vacuum" to the state described above, with the scalar field on the flat area on the left--which is also called "false vacuum" by many sources, as I noted above. This sort of confusing terminology is one reason why pop science books are not good sources: they virtually never explain their terminology or address the fact that there are multiple possible meanings of terms like "false vacuum".

 

[ChrisVer]

how is that field connected to \mathcal{R}^2 potential? I mean the scalar field potential V(\phi) doesn't seem to depend on \phi

 

[PeterDonis]

how is that field connected to $\mathcal{R}^2$ potential?

Do you mean $\phi^2$? There is no $\mathcal{R}$ anywhere. The figure I referred to describes the behavior of $\phi$ in either the entire universe (if $\phi$ is assumed to be the same everywhere), or in some chosen region of the universe that is being described (some inflation models allow different regions to have different values of $\phi$). But the potential in these models is not a function of position; it's a function of the value of the field, hence the notation $V(\phi)$.

the scalar field potential $V(\phi)$ doesn't seem to depend on ϕ

It depends on the potential. The lectures talk about different possible potentials.

 

[bapowell]

how is that field connected to \mathcal{R}^2 potential? I mean the scalar field potential V(\phi) doesn't seem to depend on \phi

R^2 inflation can be written as a scalar field in Einstein gravity via conformal transformation.