# The cause behind inflation

Hi all,

I was reading about eternal inflation however one thing that remains unclear to me is that how does one explain the force behind inflation, the word "force" is perhaps a non-technical term, the more precise term is "inflation field", the chaotic inflation model says that just perturbations caused this and that other inflated universes caused other universes, in Guth's model this force is unknown, can anyone please enlighten me on where and how this force works, any links to related papers would be very much appreciated. Thanks.

- Vikram

bapowell
The field that drives the inflationary expansion is called the inflaton field. It is a spinless (scalar) field that must have sufficient vacuum energy. The vacuum energy, when provided as a source term in Einstein's Equations, leads to a repulsive, accelerated expansion of spacetime. The force is simply that of gravity -- its repulsive nature is a result of the strange properties of the vacuum energy. So, in order to get inflation, one needs a scalar field with sufficient vacuum energy across a sufficiently large homogeneous patch of spacetime.

In the chaotic model, one has a polynomial describing the potential energy of the inflaton, for example,

$$V(\phi) = m^2 \phi^2$$

where $\phi$ is the inflaton and $m$ is a mass term. In order for this field to drive inflation, it must be initially displaced quite far from its zero energy minimum -- typically on the order of $10m_{Pl}$. Now, classically, as the universe inflates the field will roll down to its minimum, and when it gets there, inflation will end in this part of the universe. But the field is in fact a quantum field, and so it is subject to quantum fluctuations. While the field classically rolls down, quantum fluctuations can act to kick it back up. On average, they will kick the field down as often as they kick it up. But if the universe is large enough, then there are guaranteed to be regions in which the inflaton field is still displaced quite a ways from its minimum, because, although rare, the quantum fluctuations have managed to provide a net displacement against the classical rolling.

It's important to point out that Guth's original 'old' inflation and Linde's chaotic inflation rely on the same mechanism -- an inflaton field with nonzero vacuum energy. The difference lies in the functional form of the potential energy -- Guth originally envisioned the inflaton as evolving in a 'Mexican hat' potential (like those of the Higgs fields in GUTs) towards a true minimum. It is generically much more difficult for eternal inflation to occur with this kind of potential (technically this is because the false vacuum region is not a dynamical attractor.)

There are obviously plenty of papers on these topics -- which in particular are you interested in learning more about?

I am confused because you mention eternal inflation and the inflaton. I understood that the inflaton inflation lasted only a very brief time? Or are you saying that this same inflation continues now and is responsible for the dark energy expansion that we see now?

http://en.wikipedia.org/wiki/Dark_energy

bapowell
No, sorry for the confusion. Eternal inflation and the present day accelerated expansion are separate concepts. It is important to distinguish our observable universe from the universe -- of which our observable universe is but one part. The idea of eternal inflation conceives of the entire universe undergoing inflation. Due to quantum fluctuations, parts of the universe will stop inflating, while others will continue to do so. Our observable universe is one of those that stopped inflating. The idea that other regions of the universe continue to inflate now, and more importantly, that the volume of the inflating regions grows without bound relative to the non-inflating regions, is termed eternal inflation.

What's important is that our observable universe stopped inflating at some point.
The fact that our observable universe is now, again, undergoing accelerated expansion is inconsequential so long as the rate of expansion is less than those regions undergoing eternal inflation.

Guth describes eternal inflation occuring if the false vacuum expands faster than it decays into the true vacuum. Is this a seperate mechanism to the quanutm kicks (up the hill) ?

bapowell
Guth describes eternal inflation occuring if the false vacuum expands faster than it decays into the true vacuum. Is this a seperate mechanism to the quanutm kicks (up the hill) ?
Yes, it its. Thanks for pointing this out! Indeed, this is why Guth's original implementation of inflation within our observable universe failed -- the nucleation rate of true vacua is too slow and the more quickly expanding false vacuum region comes to dominate the volume of the universe. This is true of inflationary potentials that involve a 1st-order phase transition, in which the field must tunnel through a potential barrier in order to reach the true minimum. It was incorrect for me to state earlier that Guth's original model has a difficult time eternally inflating. The Mexican hat potentials, which are 2nd-order phase transitions, do indeed have a hard time but these were not the potentials Guth originally played with. In fact, inflation driven by these potentials came to be known as 'new' inflation (introduced by Linde, Albrecht and Steinhardt, Shafi and Vilenkin, and others), to Guth's 1st-order 'old' inflation. Apologies.

bapowell
Not sure what super inflation is though, anyone know?
Inflation that results from an equation of state parameter, $w = p/\rho < -1$, giving $\dot{\rho} > 0$.

No, sorry for the confusion. Eternal inflation and the present day accelerated expansion are separate concepts. It is important to distinguish our observable universe from the universe -- of which our observable universe is but one part. The idea of eternal inflation conceives of the entire universe undergoing inflation. Due to quantum fluctuations, parts of the universe will stop inflating, while others will continue to do so. Our observable universe is one of those that stopped inflating. The idea that other regions of the universe continue to inflate now, and more importantly, that the volume of the inflating regions grows without bound relative to the non-inflating regions, is termed eternal inflation.

What's important is that our observable universe stopped inflating at some point.
The fact that our observable universe is now, again, undergoing accelerated expansion is inconsequential so long as the rate of expansion is less than those regions undergoing eternal inflation.

bppowell thanks for clarification! This is similar to what I was proposing in my first ever post here (which got locked btw :) ) the possibility that in an almost infinite universe, much bigger than the observable universe, that inflation might still be still taking place and perhaps even driving the dark energy expansion that we see in the rest of universe. This is very interesting. I really like it because it doesnt confine creation to a single one and only event once thoughout all time, but instead adds a little homogeniety in time as well as what we expect to see in space.

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