Multiverse reduction in the new Hawking/Hertog model?

[Agrippa]

Hawking and Hertog's new paper "A Smooth Exit from Eternal Inflation?" does away with the infinite multiverse of Hawking's previous theory and proposes a cosmology that predicts "a simpler and finite universe".

But I can't figure out the extent of this reduction to a "simpler and finite" universe. In the previous theory, the fundamental constants varied in that different pocket universes had different values for the masses of elementary particles, the fine-structure constant, and the cosmological constant. But what about the new theory?

I can't find any clear answer to this. Many pop sci followups are claiming that "the laws of nature are the same in each pocket universe" but it is not made clear what this means, nor is this claim explicitly found in the original paper.

Can anyone shed any light on this? Do the pocket universes in the new model still have different constants or not? Thanks!

 

[kimbyd]

Hawking and Hertog's new paper "A Smooth Exit from Eternal Inflation?" does away with the infinite multiverse of Hawking's previous theory and proposes a cosmology that predicts "a simpler and finite universe".

But I can't figure out the extent of this reduction to a "simpler and finite" universe. In the previous theory, the fundamental constants varied in that different pocket universes had different values for the masses of elementary particles, the fine-structure constant, and the cosmological constant. But what about the new theory?

I can't find any clear answer to this. Many pop sci followups are claiming that "the laws of nature are the same in each pocket universe" but it is not made clear what this means, nor is this claim explicitly found in the original paper.

Can anyone shed any light on this? Do the pocket universes in the new model still have different constants or not? Thanks!

The typical description for how the low-energy physical constants are determined rests upon the concept of spontaneous symmetry breaking. At sufficiently high temperatures, the fundamental physics observes a particular symmetry, but as temperatures drop that symmetry is broken. An analogy that is often used is a material which can form a permanent magnet. In the absence of an external magnetic field, at high temperatures the magnetic moments of the individual atoms will be arranged randomly, so that there is no preferred direction in the material. As the magnet cools, the magnetic moments of nearby atoms tend to align together, such that as the magnet cools regions within the magnet forms where the magnetic moments of the atoms are all pointing in the same direction. This is a broken symmetry: no longer is the material rotationally-symmetric, as the magnetic field points in a specific direction. The direction field in the domain points is completely random (assuming there isn't some external magnetic field setting the value).

Spontaneous symmetry breaking is a similar concept, but instead of directions in space there are different values of fundamental constants (some of the fundamental constants even look like angles). These contribute to things like the masses of the weak force carriers (W and Z bosons), whose values influence nuclear reactions.

In the context of this paper, it predicts a large-scale homogeneous universe. Such a universe can't really have spontaneous symmetry breaking events happen after inflation ends, because between the time inflation ends and the CMB is emitted, different locations on the CMB have not had time to communicate. So if there were such an event, its results would necessarily be different in different locations within the observable universe. There is no evidence of this.

So if there was a spontaneous symmetry breaking event which decided the values of these fundamental constants, it must have occurred during or before inflation (note: the model in the paper doesn't actually have a "before" inflation, but during is in principle possible, as long as it was very early-on). This paper claims that the resultant universe is too homogeneous for such a thing to cause different regions to have different low-energy physical laws.

 

[Agrippa]

The typical description for how the low-energy physical constants are determined rests upon the concept of spontaneous symmetry breaking. At sufficiently high temperatures, the fundamental physics observes a particular symmetry, but as temperatures drop that symmetry is broken.
[...]
In the context of this paper, it predicts a large-scale homogeneous universe. Such a universe can't really have spontaneous symmetry breaking events happen after inflation ends,
[...]
So if there was a spontaneous symmetry breaking event which decided the values of these fundamental constants, it must have occurred during or before inflation (note: the model in the paper doesn't actually have a "before" inflation, but during is in principle possible, as long as it was very early-on). This paper claims that the resultant universe is too homogeneous for such a thing to cause different regions to have different low-energy physical laws.

Thanks, that's helpful (I've quoted the parts I've understood). My understanding is now that:

The earlier model predicted that spontaneous symmetry breaking events happen many times after inflation, and these events somehow ensure that the various pocket universes that subsequently arise will have different low-energy physical laws.

The new model predicts that there is only one spontaneous symmetry breaking event, which happened during inflation, and this event somehow ensures that the various pocket universes that subsequently arise all have identical (or close-to-identical?) low-energy physical laws?

 

[kimbyd]

The earlier model predicted that spontaneous symmetry breaking events happen many times after inflation, and these events somehow ensure that the various pocket universes that subsequently arise will have different low-energy physical laws.

The idea here is that the large-scale inhomogeneity allows such events to happen many times.

The new model predicts that there is only one spontaneous symmetry breaking event, which happened during inflation, and this event somehow ensures that the various pocket universes that subsequently arise all have identical (or close-to-identical?) low-energy physical laws?

I think it's more that if they happened late enough that their future light cone was smaller than the observable universe, they would be observable. There could easily be multiple events, but only early-on.

 

[Agrippa]

The idea here is that the large-scale inhomogeneity allows such events to happen many times.

Okay I think I get that. In the old model, the large-scale inhomogeneity of expansion creates post-inflation spontaneous symmetry breaking events, which cause pocket-universes with distinct constants.

I think it's more that if they happened late enough that their future light cone was smaller than the observable universe, they would be observable. There could easily be multiple events, but only early-on.

I don't quite understand this statement. I would like to set aside the question of whether these other pocket universes are observable. I am interested in the question of whether these other pocket universes have different constants, according to the new model.

It seems the new model has:
(i) multiple spontaneous symmetry breaking events but only during inflation.
(ii) large-scale homogeneity of expansion.

You've claimed (if I've understood) that:
(iii) What causes multiple pocket-universes with differing constants is multiple spontaneous symmetry breaking events.

What's puzzling me is that if the new model has (i) and (iii) is true, then it follows that the new model has multiple pocket-universes with differing constants. (Sorry if I'm just being slow here!)

 

[kimbyd]

There are two main constraints at play here:
1) In order for there to be a spontaneous symmetry breaking event, you need high energy (e.g. a high-temperature system that cools down).
2) If the event happens too late, it will be observable through different locations in the observable universe having different values, or through defects like cosmic superstrings.

Inflation itself tends to rapidly cool the universe, which limits the ability for any symmetry breaking to occur after a very short time. If the properties of inflation are such that the very earliest moments are high enough in temperature, you might get some spontaneous symmetry breaking as that high-temperature environment cools. But once it cools that will stop (most of the history of inflation is at effectively zero temperature, regardless of the initial temperature). Once inflation ends and the universe reheats, you could in principle get some new symmetry breaking, but, as I stated earlier, that would be observable.

In eternal inflation it still might be possible to get symmetry breaking events because the field energy tends to increase periodically, which might supply enough energy to the system to allow such an event. I could imagine a situation where at high enough energies, the zero-point fluctuations in the field result in localized temperatures high enough to cause symmetry breaking (zero-point fluctuations would be a small fraction of the field energy, but if the field energy were high enough, they might be sufficient). These localized temperatures would cool almost instantly, but that might be enough.

I think this paper is stating that fluctuations that occur during inflation can't cause large-scale inhomogeneities, and for related reasons can't cause the localized energy difference which would allow for spontaneous symmetry breaking events to recur.

 

[Agrippa]

I think this paper is stating that fluctuations that occur during inflation can't cause large-scale inhomogeneities, and for related reasons can't cause the localized energy difference which would allow for spontaneous symmetry breaking events to recur.

Interesting. The way I understand it now is that...

(i) For different pocket universes to have different low-energy laws, you need recurrence of post-inflation spontaneous symmetry breaking events.

(ii) The new paper states that fluctuations that occur during inflation can't cause large-scale inhomogeneities, and for related reasons can't cause the localized energy difference which would allow for spontaneous symmetry breaking events to recur.

Incidentally, do you understand how these spontaneous symmetry breaking events can actually cause the force-carrying particles to have different mass (for e.g.) in different pocket universes?

 

[JMz]

What about the electroweak symmetry breaking? That happens long before CMB emission (necessarily!), but my understanding is that it's after either most or all of the inflationary epoch. (1) Is that compatible with BB nucleosynthesis and other observable consequences? (2) Is that compatible with Hawking's paper?

 

[kimbyd]

What about the electroweak symmetry breaking? That happens long before CMB emission (necessarily!), but my understanding is that it's after either most or all of the inflationary epoch. (1) Is that compatible with BB nucleosynthesis and other observable consequences? (2) Is that compatible with Hawking's paper?

If it were spontaneous and after the inflationary epoch, then the domain walls would be on the order of 1 degree on the sky (this is the distance that light rays could travel between the end of inflation and the emission of the CMB).

If electroweak symmetry breaking happened after the end of inflation, it had to be an explicit symmetry breaking event. That is, the properties of the universe at the time inflation ended would have had to explicitly pick out the values of the constants that would eventually result.

One way to visualize the two situations is to imagine a table with a bunch of rods connected to one another with springs, and connected to ball joints on the table so that the individual rods could point in any direction. At high temperatures, with each rod having lots of kinetic energy, the rods themselves will bounce around in all directions, and energy will be continually shifting between the compression/tension on the springs and the motions of the rods. As the system cools, there won't be enough energy to move the rods or compress/stretch the springs, so the rods will tend to want to lay flat on the table all in the same direction. The direction itself is random, but once they've fallen a specific direction will be selected. That's spontaneous symmetry breaking.

Explicit symmetry breaking happens if the table is tilted, so that the rods want to lie in the downward direction.

It's entirely plausible that the electroweak symmetry breaking could be either situation, but the second situation requires that it couple to some other symmetry that has already been broken (the table has been tilted).

Much of the discussion about which types of theories beyond the standard model should be examined can be categorized as one of the above two approaches. The first suggests that many things are possible and there are random outcomes (so that the prevailing picture is of a diverse universe where many different kinds of things happen). The second suggests that there really is one minimum-energy state, and the early universe had a structure that was such that it was able to land in that minimum-energy state.

 

[PeterDonis]

If electroweak symmetry breaking happened after the end of inflation, it had to be an explicit symmetry breaking event.

Can you give some more details on why this must be the case?

 

[JMz]

Thanks, @kimbyd. FWIW, I had intended to ask only about spontaneous symmetry breaking, but in an epoch after which all of the now-observable CMB would come from one domain.

 

[kimbyd]

Can you give some more details on why this must be the case?

The content of the quoted post attempts this explanation. Is there any specific part of that explanation that you think could be fleshed out more?

 

[PeterDonis]

The content of the quoted post attempts this explanation.

Your statement is, in the terms of the analogy you give in your post, that if electroweak symmetry breaking occurs after the end of inflation, the table must have been tilted. I don't see why that must be the case. The rods will settle into some position as temperature drops whether the table is tilted or not.

 

[kimbyd]

Your statement is, in the terms of the analogy you give in your post, that if electroweak symmetry breaking occurs after the end of inflation, the table must have been tilted. I don't see why that must be the case. The rods will settle into some position as temperature drops whether the table is tilted or not.

The light cone for an event which occurred at the time of reheating is about 1 degree on the sky at the time the CMB was emitted. Spontaneous symmetry breaking which occur late can't spread further than that.

 

[PeterDonis]

The light cone for an event which occurred at the time of reheating is about 1 degree on the sky at the time the CMB was emitted. Spontaneous symmetry breaking which occur late can't spread further than that.

Ah, I see; the volume of the observable universe is too large to all be one spontaneous symmetry breaking region.

 

[JMz]

So does this mean that any such breaking had to occur much earlier than the end of inflation, or just not after it?

 

[kimbyd]

So does this mean that any such breaking had to occur much earlier than the end of inflation, or just not after it?

It had to occur some amount of time before the end of inflation. Inflation is absurdly rapid, however, so we're only talking about a minuscule fraction of a second.

The limit is on the amount of expansion, which in inflationary terms is stated as the number of e-foldings (inflation is an approximately exponential expansion given by $e^{Ht}$, and $Ht$ is the number of e-foldings). I don't know the exact number required, but it's probably close to the minimum number of e-foldings required for inflation to explain other aspects of our universe, which is around 60-70.

The inflation model cited in the OP favors shorter inflation, so it's likely any spontaneousspontaneo breaking would have had to happen right near the start.

 

[kimbyd]

Also, one point that I mentioned in passing, but thought I would elaborate on: during inflation, $H$ would have been (very approximately) around $10^{30}s^{-1}$, so that 60-70 e-foldings of inflation would have taken about $10^{-28}$ seconds.

So, to sum up what I've been arguing:
1) In order for us to not observe spontaneous symmetry breaking, it had to happen fairly early (probably tens of e-foldings before the end of inflation).
2) The inflation model proposed can't ever produce spontaneous symmetry breaking except right when it starts.

 

[JMz]

Also, one point that I mentioned in passing, but thought I would elaborate on: during inflation, $H$ would have been (very approximately) around $10^{30}$, so that 60-70 e-foldings of inflation would have taken about $10^{-28}$ seconds.

So, to sum up what I've been arguing:
1) In order for us to not observe spontaneous symmetry breaking, it had to happen fairly early (probably tens of e-foldings before the end of inflation).
2) The inflation model proposed can't ever produce spontaneous symmetry breaking except right when it starts.

Understood, and thanks.

 

[George Jones]

1) In order for us to not observe spontaneous symmetry breaking, it had to happen fairly early (probably tens of e-foldings before the end of inflation).

Electroweak physics predicts the temperature/energy at which the electroweak phase transition occurs. For standard models of inflation and reheating, this temperature occurs after inflation and reheating.

From the book "Relativistic Cosmology" by Ellis, Maartens, and MacCallum:

 

[JMz]

Electroweak physics predicts the temperature/energy at which the electroweak phase transition occurs. For standard models of inflation and reheating, this temperature occurs after inflation and reheating.

From the book "Relativistic Cosmology" by Ellis, Maartens, and MacCallum:

Nice. Two questions: It states that photon decoupling occurred ~ 40,000 years, not ~ 400,000, and the dark ages started at 100,000. But the CMB seems to date from 400,000, or a bit less. What's up there?

Second, if electroweak decay happens long after inflation, does that mean that we have clear observational evidence (from the CMB, if nothing else) that there is not spontaneous symmetry breaking -- or at least that everything observable was part of a single domain?

 

[George Jones]

Nice. Two questions: It states that photon decoupling occurred ~ 40,000 years, not ~ 400,000, and the dark ages started at 100,000. But the CMB seems to date from 400,000, or a bit less. What's up there?

Typo (I think).

Second, if electroweak decay happens long after inflation, does that mean that we have clear observational evidence (from the CMB, if nothing else) that there is not spontaneous symmetry breaking -- or at least that everything observable was part of a single domain?

@kimbyd makes an interesting point with respect to this. I don't know the answer, but I do not think that this is observational evidence for a lack of symmetry breaking.

It seems that "bubbles" nucleate (form) and then join?

 

[JMz]

Typo (I think).
@kimbyd makes an interesting point with respect to this. I don't know the answer, but I do not think that this is observational evidence for a lack of symmetry breaking.

It seems that "bubbles" nucleate (form) and then join?

I'll let her weigh in. I would have expected that joining would be dramatic event for which we would see evidence.

 

[kimbyd]

Electroweak physics predicts the temperature/energy at which the electroweak phase transition occurs. For standard models of inflation and reheating, this temperature occurs after inflation and reheating.

From the book "Relativistic Cosmology" by Ellis, Maartens, and MacCallum:

The electroweak phase transition is distinct from the spontaneous symmetry breaking event which sets the masses of the W and Z bosons.

The electroweak phase transition occurs when weak force interactions are no longer rapid, and its temperature is a function of the masses of the W and Z bosons.

The time on that graph most likely associated with the spontaneous symmetry breaking event which set the masses of the W and Z bosons is the grand-unification time, which is stated with a question mark as this is still uncertain (and happens at higher temperatures than are produced during reheating).

 

[PeterDonis]

The electroweak phase transition is distinct from the spontaneous symmetry breaking event which sets the masses of the W and Z bosons.

I always thought these were the same. In the analogy you gave earlier in the thread, the rods settling down into a certain direction on the table is the symmetry breaking event; and the direction of the rods corresponds to the Weinberg angle, which sets the W and Z boson masses and separates out the weak and electromagnetic interactions, and is the phase transition.

 

[JMz]

The electroweak phase transition is distinct from the spontaneous symmetry breaking event which sets the masses of the W and Z bosons.

The electroweak phase transition occurs when weak force interactions are no longer rapid, and its temperature is a function of the masses of the W and Z bosons.

The time on that graph most likely associated with the spontaneous symmetry breaking event which set the masses of the W and Z bosons is the grand-unification time, which is stated with a question mark as this is still uncertain (and happens at higher temperatures than are produced during reheating).

Thanks, @kimbyd. My own question here was about the separation of electroweak into E&M and weak. That presumably occurs long after GU, right? But well before the end of inflation, according to the 1-degree-on-the-sky limit.

 

[JMz]

I always thought these were the same.

Yes, that summarizes my confusion as well.

 

[PeterDonis]

For example, the paper linked to below gives the scale of electroweak symmetry breaking as 246 GeV in the simplest model, and in any case around the TeV scale:

https://arxiv.org/abs/hep-ph/9505296

This appears to be describing EWSB and the electroweak phase transition as the same event.

 

[kimbyd]

For example, the paper linked to below gives the scale of electroweak symmetry breaking as 246 GeV in the simplest model, and in any case around the TeV scale:

https://arxiv.org/abs/hep-ph/9505296

This appears to be describing EWSB and the electroweak phase transition as the same event.

Hmm. I think I was misunderstanding what was meant by the electroweak phase transition. I should have looked more carefully at the energy scales, as the temperature at which the weak nuclear force is no longer rapid is closer to 1MeV, not 1TeV. The electroweak symmetry breaking event indeed would have been around 1TeV (in order of magnitude) as this is roughly around the mass of the Higgs boson.

What this discussion tells me is that event necessarily had to be an explicit symmetry breaking, because if the outcome were random, it couldn't have propagated throughout the entire observational universe, and would have led to a large number of observational effects.