# Slow roll inflation -layperson question

• a dull boy
In summary, the early conception of inflation involved a bubble nucleation event where the field jumped spontaneously from a state of higher PE to vacuum, resulting in bubbles that expanded and coalesced to complete inflation. However, this led to problems with homogeneity. To address this, "new" inflation was proposed where the transition is not first-order, but second-order or slightly first-order. This avoids the need for violent bubble collisions and allows for the entire observable universe to fit inside a single bubble. Therefore, the slow roll phase transition occurs within an expanding bubble, but we need not talk about bubbles or their dynamics as the universe is effectively infinite within the bubble.
a dull boy
Dear PF,

I'm trying to understand slow roll inflation from a layperson view, and I think my current understanding is mistaken. If a bubble of matter is trapped in a local minimum PE state, and begins to roll down a hill to a lower PE state, it strikes me that bubble will expand in size the same way a bubble of air trapped in water expands when it reaches the surface. But I don't think this is at all how cosmologists explain inflation. Could someone help?

Thanks, A dull boy

What exactly do you mean by "when it reaches the surface"?

The early conception of inflation indeed was understood as a bubble nucleation event: the inflationary phase transition was "first-order" so that the field jumped spontaneously from the state of higher PE to vacuum, creating bubbles of vacuum in the inflating region. The bubbles would then expand outwards at near the speed of light, converting higher PE regions to vacuum. Bubbles then coalesced to complete the inflationary event in our observable universe. As you might know, there are serious problems with this sequence of events, namely that the resulting universe would be strongly inhomogeneous on account of the bubble collisions.

To address this problem, "new" inflation was quickly proposed by Linde and others. Here, the transition is not first-order, but second-order, or at least only very slightly first-order. Instead of jumping directly to the vacuum, the field either slowly rolls off the local maximum towards the vacuum (in the case of second order), or tunnels through the barrier and then slowly rolls to the vacuum (in the case of lightly first order). Here, it doesn't help so much to think in terms of bubble nucleation, although that is very possibly what is happening (the Hawking-Moss instanton describes bubble nucleation appropriate to second-order transitions). The reason is that the whole of the observable universe after inflation fits inside a single bubble; this is because the inflationary phase transition takes so long to complete (it is a "slow" roll after all). This solves the problems of old first-order inflation by avoiding the need for violent bubble collisions.

So, in summary, while the slow roll phase transition does likely occur inside an expanding bubble (where the PE inside the bubble is decreasing more rapidly than that outside), because the whole of the observable universe fits inside the bubble, we need not talk about bubbles or worry about their dynamics. We can instead work within the bubble where the universe is effectively infinite.

Thank you very much, I understand this much better now.

## 1. What is slow roll inflation?

Slow roll inflation is a theory that describes the rapid expansion of the universe in the early stages of its development. It proposes that there was a period of time where the universe expanded at an exponential rate due to a hypothetical field called the inflaton field. This resulted in the universe becoming much larger and much more uniform than it was before.

## 2. How does slow roll inflation explain the flatness problem?

The flatness problem is the observation that the universe appears to be very flat on a large scale, meaning that the density of matter is almost exactly equal to the critical density needed for the universe to be flat. Slow roll inflation provides an explanation for this by proposing that the rapid expansion of the universe during inflation smoothed out any irregularities in the density of matter, resulting in a flat universe.

## 3. What is the role of the inflaton field in slow roll inflation?

The inflaton field is a hypothetical field that is thought to have existed during the early stages of the universe. It is responsible for driving the rapid expansion of the universe during inflation. As the universe expanded, the energy of the inflaton field decreased, eventually leading to the end of inflation and the beginning of the hot Big Bang.

## 4. How does slow roll inflation solve the horizon problem?

The horizon problem is the observation that the universe appears to be the same temperature in all directions, despite the fact that these regions would not have had enough time to interact and reach thermal equilibrium. Slow roll inflation provides an explanation for this by proposing that the rapid expansion during inflation allowed these regions to interact and reach thermal equilibrium before inflation ended, resulting in the observed uniformity in temperature.

## 5. What evidence supports the theory of slow roll inflation?

There are several lines of evidence that support the theory of slow roll inflation. These include the observed flatness of the universe, the uniformity of the cosmic microwave background radiation, and the presence of primordial gravitational waves. Additionally, slow roll inflation is consistent with other well-established theories such as general relativity and quantum mechanics.

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