Cosmological electroweak phase transition

[Carlos L. Janer]

There is a question that has been bugging and puzzling me for a long time and I wondered if somebody could help me to figure out what the answer is or where I am not thinking straight.

Let us assume that the standard model of particle physics is more "right" than "wrong" and there is no such a thing as a supersymmetry between fundamental fermions and bosons. If this were the case, then we would have that when the cosmological EW phase transition took place, strong interactions were already differentiated from EW interactions.

The idea of an electro-weak phase transition seems to be borrowed from condensed matter physics, more precisely, from the physics of critical phenomena. I have always assumed that the analogy is more fundamental than formal (maybe I am wrong). If this is true, the whole universe was described by a single "partition function". I am not quite sure how quarks, neutrinos and electrons could have a common temperature (and exchange energy-momentum) since they were all massless particles, but that is not very important for the moment.

It is hard for me to believe that this phase transition could be "first order" instead of "second order" since the former are characterized by a finite range correlation length wheareas the latter by an infinite correlation length. However it seems that this phase transition has to be "first order" because, otherwise, baryon asymmetry could not be convicingly explained.

But if the EW phase transition were "first order", should not Higgs field have different expectation values in different regions of the universe? If this were the case, should not these different parts of the univese have different physical properties?

I would appreciate it very much if anyone could tell me where I am wrong.

 

[fresh_42]

But if the EW phase transition were "first order", should not Higgs field have different expectation values in different regions of the universe? If this were the case, should not these different parts of the univese have different physical properties?

Funny coincidence: just today I've read the following article:

http://phys.org/news/2017-01-multiple-standard-hierarchy-problem.html
based on from July 22, 2016 (https://arxiv.org/abs/1607.06821)

Nnaturalness
Nima Arkani-Hamed, Timothy Cohen, Raffaele Tito D'Agnolo, Anson Hook, Hyung Do Kim, David Pinner

We present a new mechanism to stabilize the electroweak hierarchy. We introduce $N$ copies of the Standard Model with varying values of the Higgs mass parameter. This generically yields a sector whose weak scale is parametrically removed from the cutoff by a factor of $1/\sqrt{N}.$ Ensuring that reheating deposits a majority of the total energy density into this lightest sector requires a modification of the standard cosmological history, providing a powerful probe of the mechanism. Current and near-future experiments will explore much of the natural parameter space. Furthermore, supersymmetric completions which preserve grand unification predict superpartners with mass below $m_W \times M_{pl}/M_{GUT}\,∼\,10 \,TeV.$

 

[Carlos L. Janer]

Funny coincidence: just today I've read the following article:

http://phys.org/news/2017-01-multiple-standard-hierarchy-problem.html
based on from July 22, 2016 (https://arxiv.org/abs/1607.06821)

Nnaturalness
Nima Arkani-Hamed, Timothy Cohen, Raffaele Tito D'Agnolo, Anson Hook, Hyung Do Kim, David Pinner

Thanks for the links! I will take a look and see if I understand the papers.

 

[PeterDonis]

I am not quite sure how quarks, neutrinos and electrons could have a common temperature (and exchange energy-momentum) since they were all massless particles

Why is masslessness a problem? Remember that these are not little billard balls; they're quantum field excitations. They interact via the electroweak interaction, i.e., by means of other quantum field excitations. None of that requires any of the fields to have nonzero mass.

 

[PeterDonis]

I would appreciate it very much if anyone could tell me where I am wrong.

As I understand it, the question you are asking is a genuine open question that is still being researched (the papers fresh42 linked to are part of that research).

 

[Carlos L. Janer]

As I understand it, the question you are asking is a genuine open question that is still being researched (the papers fresh42 linked to are part of that research).

Ok, I thought there was something I was not getting right. However, the whole observable universe seems to have everywhere the same local physical properties we measure around us. Those parts where the Higgs field vacuum expectation values could be different (in actual fact, when I posted my question, I was tacitly assuming that the VEV were the same and, perhaps, the phase was different) should lie beyond our horizon. Am I wrong?

 

[PeterDonis]

the whole observable universe seems to have everywhere the same local physical properties we measure around us. Those parts where the Higgs field vacuum expectation values could be different (in actual fact, when I posted my question, I was tacitly assuming that the VEV were the same and, perhaps, the phase was different) should lie beyond our horizon.

Yes, I believe this is correct. The open issue, as I understand it, is how that can be true if the phase transition was first order.

 

[Carlos L. Janer]

Yes, I believe this is correct.

Thanks for your reply.

 

[Orodruin]

because, otherwise, baryon asymmetry could not be convicingly explained.

Let me just add that it is generally believed that baryon asymmetry cannot be explained by the Standard Model through electroweak baryogenesis regardless of the type of phase transition. The CP-violating phase in the CKM matrix is way too small for that to be possible. In fact, this is a strong argument for something beyond the Standard Model to exist.

 

[Carlos L. Janer]

Let me just add that it is generally believed that baryon asymmetry cannot be explained by the Standard Model through electroweak baryogenesis regardless of the type of phase transition. The CP-violating phase in the CKM matrix is way too small for that to be possible. In fact, this is a strong argument for something beyond the Standard Model to exist.

OK but what is bothering me is this: Could our observable universe be in thermodynamic equilibrium at whatever energy scale the W and EM interactions decoupled? Or was it way too big? What I do not really know if SSB is just an artifact to explain the elementary particle masses (it does not seem very likely to me since Higgs boson has been detected) or it actually was a true thermodynamic phase transition?

 

[PeterDonis]

Could our observable universe be in thermodynamic equilibrium at whatever energy scale the W and EM interactions decoupled? Or was it way too big?

That is one of the problems that inflation models claim to solve (the general term for it is the "horizon problem"; it's not limited to the EW phase transition). Without inflation, yes, the observable universe would have been too big at the phase transition for all of its parts to have been in causal contact, so it could not have been in thermal equilibrium. With inflation, because the observable universe at the phase transition would have been inflated from a much smaller previous state, it would have had time to thermalize before it was inflated, and inflation preserves thermal equilibrium, so it would have been in equilibrium at the phase transition.

This, however, is a separate problem from the problem of why the Higgs has the same VEV throughout the observable universe if the phase transition was first order. Inflation models don't solve the latter problem.

 

[Carlos L. Janer]

That is one of the problems that inflation models claim to solve (the general term for it is the "horizon problem"; it's not limited to the EW phase transition). Without inflation, yes, the observable universe would have been too big at the phase transition for all of its parts to have been in causal contact, so it could not have been in thermal equilibrium. With inflation, because the observable universe at the phase transition would have been inflated from a much smaller previous state, it would have had time to thermalize before it was inflated, and inflation preserves thermal equilibrium, so it would have been in equilibrium at the phase transition.

This, however, is a separate problem from the problem of why the Higgs has the same VEV throughout the observable universe if the phase transition was first order. Inflation models don't solve the latter problem.

I am not familiar with the standard cosmological model but I can understand that the "universe" could be at "thermal equilibrium" right after the inflationary epoch. However, if it started to cool down right afterwards, it seems very unreasonable to me to assume that this process heppened everywhere exactly in the same way. I am going to speculate so I may be talking nonsense: I would tend to think that the vacuum state would change smoothly (at least its phase) across the whole "universe" (whatever this word means, because it does not seem to be our observable universe).

 

[PeterDonis]

if it started to cool down right afterwards, it seems very unreasonable to me to assume that this process heppened everywhere exactly in the same way

It didn't. We know that because we know our present universe is not perfectly homogeneous; the matter in it has clumped into galaxies and stars and planets and us. So there must have been some inhomogeneities in the Big Bang. But they could have been very small at that time, since the clumping that has taken place over the past 13.7 billion years could have happened via gravity from very small variations in density at the start.

I would tend to think that the vacuum state would change smoothly (at least its phase) across the whole "universe"

The EW phase transition is not purely a matter of a vacuum state. It involves the VEV of the Higgs field, but the other Standard Model fields were not anywhere close to being in a vacuum state--they were thermally populated at a high temperature and density. The inhomogeneities could have been confined to the fields that were thermally populated, leaving the Higgs VEV uniform.

 

[Orodruin]

I am not familiar with the standard cosmological model but I can understand that the "universe" could be at "thermal equilibrium" right after the inflationary epoch.

"Right after" is usually not the case. Right after inflation the Universe is completely empty apart from the inflaton field. The decay of the inflaton field creates a large number of particles that start interacting and enter thermal equilibrium with each other. This process is called reheating.

I would tend to think that the vacuum state would change smoothly (at least its phase) across the whole "universe" (whatever this word means, because it does not seem to be our observable universe).

This is not necessarily the case and it depends on how the minimum at a non-zero value of the Higgs field develops as temperature decreases. It would generally be possible to develop this minimum with or without a barrier that the field has to tunnel through.

 

[Carlos L. Janer]

The EW phase transition is not purely a matter of a vacuum state. It involves the VEV of the Higgs field, but the other Standard Model fields were not anywhere close to being in a vacuum state--they were thermally populated at a high temperature and density. The inhomogeneities could have been confined to the fields that were thermally populated, leaving the Higgs VEV uniform.

I am afraid that I cannot have an informed opinion about any of this because I know next to nothing about the Lambda-CDM model. However I am starting to think that the connection between a "cosmological phase transition" and equilibrium critical phenomena is not as straightforward as I thought it was. I will work and think about this for a few weeks and will come back to this subject when/if I have anything meaningful to say.

Thank you very much to both of you, PeterDonis and Orodruin for your time.

Carlos.

 

[Carlos L. Janer]

"Right after" is usually not the case. Right after inflation the Universe is completely empty apart from the inflaton field. The decay of the inflaton field creates a large number of particles that start interacting and enter thermal equilibrium with each other. This process is called reheating.This is not necessarily the case and it depends on how the minimum at a non-zero value of the Higgs field develops as temperature decreases. It would generally be possible to develop their minimum with or without a barrier that the field has to tunnel through.

I am sorry to bother you again with this subject, but the more I think about it the less I understand it. My questions are numerous: How real is the cosmological EW phase transition suppossed to be? Did it really happen or there was a single GUT phase transition? Because if it really happened, if it is not just an artifact to produce mass, it has implications that seem paradoxical to me, to say the least:

1.- Pior to it, all fundamental fermions were massless and, correct me if I am wrong, Weyl equations described them? Parity was not a discrete symmetry of any gauged interaction? Do we have to figure out a new equation to describe their free behaviour?

2.- How do you decelarate a particle that is moving at the speed of light?

3.- Did leptons and quarks masses increased at the same rate as Higgs field VEV was becoming larger and larger? If this were a true thermodynamical phase transition, Higgs field minimum VEV would not be attained instantly, it would increase graudally as temperature dropped.

4.- I find no compelling reason to explain why Higgs field phase takes the same value at causally disconnected regions of the universe.

Sorry for posting so many questions at the same time, but I can make no sense of it. I think that I do not understand the cosmological implications of this phase transition at all.

 

[Carlos L. Janer]

Do my questions make any sense? If they do not, I would appreciate it very much if someone told me so.

 

[PeterDonis]

Pior to it, all fundamental fermions were massless

Yes.

Weyl equations described them?

What are "Weyl equations"?

Parity was not a discrete symmetry of any gauged interaction?

As far as I know, in our current model of the electroweak phase transition it does not affect the parity symmetry properties of any of the interactions.

How do you decelarate a particle that is moving at the speed of light?

The EW phase transition doesn't involve "decelerating" anything. It involves quantum fields, not particles. ("Particles" is just a useful shorthand name for certain types of quantum field states; it is not a fundamental concept in QFT and this is a case where it cannot usefully be applied.)

Did leptons and quarks masses increased at the same rate as Higgs field VEV was becoming larger and larger?

I don't know that we know an answer to this question with our current level of knowledge.

I find no compelling reason to explain why Higgs field phase takes the same value at causally disconnected regions of the universe.

In inflation models, our observable universe was causally connected before the EW phase transition, so there is nothing that needs explaining. That is one of the key things that makes inflation models useful.

 

[Carlos L. Janer]

What are "Weyl equations"?

https://en.wikipedia.org/wiki/Weyl_equation

The EW phase transition doesn't involve "decelerating" anything. It involves quantum fields, not particles. ("Particles" is just a useful shorthand name for certain types of quantum field states; it is not a fundamental concept in QFT and this is a case where it cannot usefully be applied.)

Before the EW phase transition (and afterwards) the temperature of the universe was very high, so there had to be excitations ("particles") of the different quantum fields. They all had to be massless because the Higgs field VEV was zero. My question is: what happened to these massless "excitations" when the bubbles of the new true vacuum (whose Higgs field VEV was no longer zero) formed and began to expand? Did they suddenly become aware that they "had to acquire mass"? I think that you realize that the situation is paradoxical.

 

[Orodruin]

so there had to be excitations ("particles") of the different quantum fields.

A particle is a very peculiar type of excitation. You cannot put an equal sign between particles and excited quantum field.

 

[Carlos L. Janer]

A particle is a very peculiar type of excitation. You cannot put an equal sign between particles and excited quantum field.

But why did the universe have to be devoid of such particles?

 

[Carlos L. Janer]

In inflation models, our observable universe was causally connected before the EW phase transition, so there is nothing that needs explaining. That is one of the key things that makes inflation models useful.

Our universe has regions that are causally connected to us but not among themselves.

 

[Carlos L. Janer]

I am not trying to struggle with anybody, this is not about being either "right" or "wrong". The only thing I want is to understand the things that seem paradoxical to me. They probably look paradoxical to me just because I do not have a clear understanding of what was happening.