# Higgs field in the early universe

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1. May 23, 2014

### skydivephil

As i understand it, at some point in the early unvierse, the Higgs field was off, then it swtiched on. Is this correct? I cant find when this is supposed to have happened, does anyone know?

2. May 23, 2014

### Mordred

Depends on which Supersymmetry GUT model. in the SU(5) model it correlates the breaking of SU(5) to SU(3)*SU(2)*U(1), not sure where it sits in the SO(10) GUT model. However it would be when fermions and weak guage bosons first gain mass. In the Georgi-Glashow model (outdated) which correlates to above, the break is at the GUT Epoch, or grand unification scale. roughly 1016GeV

according to Wiki
"The electromagnetic interaction was modeled with the weak interaction, whose force carriers are W and Z bosons, traversing minuscule distance, in electroweak theory (EWT). Electroweak interaction would operate at such high temperatures as soon after the presumed Big Bang, but, as the early universe cooled, split into electromagnetic and weak interactions. The strong interaction, whose force carrier is the gluon, traversing minuscule distance among quarks, is modeled in quantum chromodynamics (QCD). EWT, QCD, and the Higgs mechanism, whereby the Higgs field manifests Higgs bosons that interact with some quantum particles and thereby endow those particles with mass, comprise particle physics' Standard Model (SM). Predictions are usually made using calculational approximation methods, although such perturbation theory is inadequate to model some experimental observations (for instance bound states and solitons). Still, physicists widely accept the Standard Model as science's most experimentally confirmed theory."

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

Georgi-Glashow model SU(5)*SU(3)*SU(2)*U(1)
http://en.wikipedia.org/wiki/Georgi–Glashow_model

here is a review of various GUT models.
see section 2.4.1
http://arxiv.org/pdf/hep-ph/9402266v5.pdf

here are a couple others covering S0(10)
http://arxiv.org/pdf/0904.1556.pdf
http://pdg.lbl.gov/2...11-rev-guts.pdf [Broken]

Last edited by a moderator: May 6, 2017
3. May 23, 2014

### skydivephil

Thank you for that Modred , this look slike the same energy scale as inflation is supposed to happen. So i preumse its at the same time, is that right? Also given you say its model dependant what are the range of estimates with regards to inflaiton. do some models say before inflationa and others after or ....?

Also is this related for the motivation to suggest that the bubble universes in eternal inflation have different constants? or is that solely based upon the string theory landscape? Im not trying to argue if eternal inflaiton or string landscape is correct or not, I have no opinion, but I just want to undersdtand how these issues are related (or not). Thanks

4. May 23, 2014

### Mordred

Again this also depends on which inflation model is true, there is 60 different inflation models, including numerous Higg's inflation models. The simple answer is we don't know for sure. In the Georgi-Glashow model inflation happened slightly after at the beginning of the electroweak epoch. which follows the GUT epoch.

Not sure on the bubble universe portion however

5. May 23, 2014

### phsopher

The electroweak symmetry is restored in the Standard Model above the temerature of the order of 100 GeV. As the universe cooled down below this point the Higgs would have obtained a non-zero vacuum expectation value (VEV) giving weak gauge bosons and fermions (other than neutrinos) their masses.

It should be noted though, that since the Higgs is a light field during inflation it would also obtain a VEV in our observable patch during that era. So electroweak symmetry would have been broken during inflation as well. So the brief likely history of the Higgs would be: fist a condesate would be generated during inflation and subsequently decay after inflation is over, then the thermal bath produced by the decay of the inflaton would restore electroweak symmetry until the universe cooled down beyond 100 GeV breaking the symmetry again.

I think electroweak phase transition is covered, at least brifly, in most standard cosmology text books. For example

Physical Foundations of Cosmology by Mukhanov

6. May 23, 2014

### Mordred

isn't the value 100GeV the strong coupling constant becomes weak or strong? according to Mukhanov? if your copy is the same as mine its equation 4.3.1.

$\alpha$s is 0.13 at $\cong$100GeV

he after explains the strength of strong interactions should be come inﬁnite at q2=$\Lambda$2qcd he also explains that this is based on a one loop approximation. where he is discussing the quantum chromodynamic portion. The Higg's interactions isn't even involved at this stage

That value you described is only a descriptive for when the strong coupling becomes weak or strong. the thing is the QCD coupling constant decreases at higher portions where the QED coupling constant increases at higher temperatures. Where they converge is when they unify.

http://en.wikipedia.org/wiki/Coupling_constant#Running_coupling

the unification of the coupling constants is covered on 3.1 page 30 based on the SU(5) minimal extension of the SM model.

http://arxiv.org/pdf/hep-ph/9402266v5.pdf

edit forgot to include the Yukawa coupling, there is 3 coupling constants not two. electroweak, strong and yukawa coupling constants

I had to look for the line I needed in regards to the higgs
Introducing spontaneous symmetry breaking via the Higgs-mechanism. This introduced gauge boson masses without explicitly breaking the gauge symmetry This is the SU(5) extension. the above is the SU(3)*SU(2)*U1) portion or rather a specific part of it

Last edited: May 23, 2014
7. May 23, 2014

### Mordred

Thinking about it I don't recall any of my cosmology textbooks covering SUSY. they usually describe GUT without including super symmetry. I have 6 cosmology textbooks and I don't recall any of them even mentioning the Higg's

Mind you I haven't finished reading Linde's yet but he mentioned he made it free for distribution as its outdated
http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde

Last edited: May 23, 2014
8. May 23, 2014

### phsopher

The OP is asking when the Higgs is turned on. I interpret this to mean the time when the Higgs obtains a non-zero VEV thus breaking the electroweak symmetry and giving masses to weak gauge bosons, quarks and leptons. This happens at $T\sim \mathcal O(\text{100 GeV})$. I don't have my copy of Mukhanov with me, but in this online copy, see section 4.4.5, page 176 (I'm not sure if I'm allowed to post this link since it's for an entire book, but since it's on a university webpage I assume it's ok).

I don't understand what point you are making. The strong coupling constant becomes small roughly above the the QCD phase transition scale which is 100 MeV so QCD is perturbative at the electroweak scale (100 GeV).

I don't want to comment about Grand Unification because 1) I don't know anything about it, 2) I think GUTs and the like are speculative, for all we know SM is valid all the way up to the Planck scale$^*$ (would require top mass lower than central value to ensure stability of the vacuum, though) and 3) in my estimation this is not what the OP is after.
The electroweak phase transition happens in the pure Standard Model. You don't need SUSY or GUTs. Maybe I'm wrong that most text books cover it. I know that Mukhanov does as already established and Peacock briefly mentions it (page 305) and it was mentioned in my cosmology course so I extrapolated from these and assumed that it's discussed in some fashion in most text books.

__________________________
$^*$ Of course you still need additional sectors for inflation, dark matter, neutrino masses etc.

9. May 23, 2014

### Mordred

Fair enough like I stated earlier it depends on the model. My understanding is that neither the Gut SM nor the MSSM models work completely. Best hope being on the SO(10)

In regards to SO(10) my understanding (still studying it) the higgs turns on earlier. As well as in the MSSM minimal super symmetric model.

I guess the only correct answer is that it is anyones guess lol

10. May 23, 2014

### phsopher

Like I said I don't know anything about the GUTs so I may be well off the mark here but it was my understanding that the higgs responsible for the symmetry breaking at the GUT scale would have to be a different Higgs, that is, not the Standard Model Higgs responsible for electroweak symmetry breaking. Is this not the case? I mean, we've probed electroweak physics in accelerators so we know how that works and so in my opinion the electroweak phase transition is something that happened in the universe regardless of higher energy extensions of the standard model.

11. May 23, 2014

### Mordred

How many Higg's fields.Bosons are there lol? I certainly don't know.

see alternate models, Higgs
The Minimal Standard Model as described above is the simplest known model for the Higgs mechanism with just one Higgs field. However, an extended Higgs sector with additional Higgs particle doublets or triplets is also possible, and many extensions of the Standard Model have this feature. The non-minimal Higgs sector favoured by theory are the two-Higgs-doublet models (2HDM), which predict the existence of a quintet of scalar particles: two CP-even neutral Higgs bosons h0 and H0, a CP-odd neutral Higgs boson A0, and two charged Higgs particles H±. Supersymmetry ("SUSY") also predicts relations between the Higgs-boson masses and the masses of the gauge bosons, and could accommodate a 125 GeV/c2 neutral Higgs boson.

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

The standard model is U(1)*SU(2)*SU(3) this portion has 4 Higg's particles including its anti particle

The SU(5)*SU(3)*SU(2)*U(1) MSSM needs 12 Higg's goldstone bosons forthe lie algebra if memory serves right. However I'm still learning lie algebra so I could be wrong.

So in that sense your correct in that its a different Higg's in a way lol Not sure how the SO(10) works yet but some of the numbers I've seen on it involve 72 higgs

12. May 23, 2014

### bapowell

Why all this talk about GUTs? The OP is presumably interested in the SM Higgs which has only to do with the electroweak scale. Phsopher is correct in that the temperature-corrected potential generates a local maximum below the transition temperature. Before this time (at higher temperatures) the Higgs vacuum was symmetric and the Higgs was "off".

13. May 23, 2014

### Mordred

That's up to the OP to let us know Bapowell, some point in the early universe could very well include GUT. Either way the question is answered, and for the record I never stated Phsopher was incorrect, we were discussing if its possible the Higg's occurs earlier than the predictions of the standard model

by the way wiki has the electroweak scale at 246 GeV, makes me wonder where the difference is (not that we can trust wiki 100%)

http://en.wikipedia.org/wiki/Electroweak_scale
could this be why?

"Physically, it describes the moment in our universe evolution when electric and
weak forces differentiate. At temperature scales above 100 GeV, MSM Lagrangian exhibits the gauge symmetry:"
SU(3)c*SU(2)L*U(1)Y
SU(3)c
refers to the color symmetry and plays no role in our rendition of the electroweak phase transition."
that was why I questioned the 100GeV value in post 6

see equation 3.5
http://www.staff.science.uu.nl/~proko101/DoruSticlet_pt2.pdf

answer 246 GeV Minimal standard model, as I stated the electroweak scale depends on the model used
in the MSSM models the electroweak scale is roughly 1015
edit however the SUSY scale may be too high in the MSSM model so I wouldn't place any faith in MSSM. Least from what I've been reading

Last edited: May 23, 2014
14. May 23, 2014

### Chronos

15. May 24, 2014

### Mordred

Last edited: May 24, 2014
16. May 24, 2014

### bapowell

I think you are quoting the MSSM GUT scale there (supposing your units are GeV). What does SUSY have to do with electroweak symmetry breaking?

Last edited: May 24, 2014
17. May 24, 2014

### phsopher

What I'm getting at is that when you say that in some models the Higgs turns on earlier do you mean that other higgses turn on earlier or that the SM one does? I don't see why it would be that latter. We've probed the energies up to 10 TeV in accelerators, if new physics pushed the symmetry breaking scale to higher energies wouldn't we have seen it in accelerators? Since SM works at energies up to 10 TeV and there is a symmetry breaking phase transition at $T\sim \mathcal O(\text{100 GeV})$ in the SM then it must have happened in the early universe.

246 GeV is the vacuum expectation value of the Higgs in the broken phase. The temperature at which the transition happens depends on the masses of the Higgs, weak gauge bosons and the top quark; see Mukhanov, equation (4.137). It will be somewhat different though of the same order. Also I said of order 100 GeV though perhaps I have neglected to continue to say that throughout all my posts.

While this essay did win the first prize in the Gravity Research Foundation contest, it feels somewhat numerological to me. BICEP2 suggests 10^16 GeV. You know where else I've seen that number? It's the unification scale if you assume supersymmetry with not too heavy superpartners and SO(10) GUT. Ergo BICEP2 favors SO(10)?

Last edited: May 24, 2014
18. May 24, 2014

### Mordred

the standard model is a good low energy approximation, however it does not explain right hand neutrinos, dark matter, there is also the proton decay problem. How does it even explain the Higg's mass at 125GeV?
the SO(10) (non SUSY) model does cover right hand neutrinos. There is also numerous papers dealing with electro-weak vacuum and how it could potentially tie into inflation.
but according to you the Higgs field is and I quote "off" above the electroweak scale. If that's the case then explain these articles. How can one define OFF when it obviously has influences above 246 GeV? A different Higg's that is a poor argument.

or its off, but its not off when your talking the GUT scale, that doesn't make one iota of sense. Considering the purpose of any particle physics model is to define and explain all the particles and their interactions at any temperature scale, GUT just happens to be one of the goals in that. Their are countless papers that discuss the limitations of the standard model. I've been posting numerous papers throughout this post that all mention the standard model limitations. Why do you think the standard model has extensions?

There is plenty of research going on, that show the Higg's interactions beyond what is defined by the standard model. The first set explains what it has to do with the electro-weak symmetry breaking.

"The exact way particles in the Standard Model obtain mass is a question to which various
answers exist but none has been shown to be true in experiment. One possibility in the
Standard Model is that particles obtain mass through spontaneous symmetry breaking at
the scale of the electroweak force. Spontaneous symmetry breaking can be understood with
a \Mexican hat" depicting a potential for a particle (see fi gure 1.1) where a ball (particle)
that is initially placed at the tip of the hat (maximum potential, i.e. at high energies) and is
symmetric under rotations takes up a specifi c value when it tips of the top of the hat into the
rim; the picture is then no longer invariant under rotations. Electroweak symmetry breaking
(EWSB), also called the Higg's mechanism, is the process of spontaneous symmetry breaking
through which gauge bosons in gauge theories acquire their mass. In this mechanism, they do
so through \eating" or absorbing so-called massless Nambu{Goldstone bosons. The simplest
implementation of this mechanism is addition of an extra Higg's fi eld to the Standard Model.

http://phys.onmybike.nl/StrongEWSB.pdf

here is a book on it
"Electroweak Symmetry Breaking and New Physics at the TeV Scale"
http://www.worldscientific.com/worldscibooks/10.1142/3073

New Approaches to ElectroWeak Symmetry Breaking
http://lpsc.in2p3.fr/GDR-SUSY/tutorial_Annecy06/EWSB_1.pdf

ASI Lectures on Electroweak Symmetry Breaking from Extra Dimensions
http://arxiv.org/abs/hep-ph/0510275

http://arxiv.org/abs/hep-ph/9912343
"Electroweak symmetry breaking remains the foremost problem facing elementary particle
physics at this moment. We expect to come to understand it in scientific detail in the
next decade with the Tevatron and the LHC"
http://arxiv.org/pdf/hep-ph/9912343v3.pdf

Implications of LHC results for TeV-scale physics: signals of electroweak symmetry breaking
https://indico.cern.ch/event/173388/material/0/0.pdf

Electroweak Vacuum Stability in light of BICEP2
http://arxiv.org/abs/1403.6786
"Electroweak Vacuum (In)Stability in an Inflationary Universe"
http://arxiv.org/abs/1301.2846
"Higgs mass implications on the stability of the electroweak vacuum"
http://arxiv.org/pdf/1112.3022.pdf

19. May 24, 2014

### Mordred

.

The standard model only uses one Higg's field, The calculation of 246 Gev is only with one Higg's field. The research papers I posted in the previous threads, show the relations with the other potential Higg's fields and possibly the seesaw mechanism. (mexican hat).

keep in mind I was very clear that it depends on which model. The choice of models favored is up to the individual. My take is the Higg's sector has a lot of open questions, and more research is needed to truly make any statements one way or the other.

Last edited: May 24, 2014
20. May 24, 2014

### bapowell

Slow down Mordred. Nobody is saying that the SM is complete, and that there isn't important unknown physics happening at and above the GUT scale. All I'm saying is that above the electroweak scale, the Higgs field responsible for breaking electroweak symmetry is *by definition* off, in the sense that the symmetry is restored. This is absolutely true at the GUT scale, as evidenced by the fact that GUT symmetry breaking occurs many orders of magnitude above the electroweak scale. Phsopher is saying the same thing: the Higgs is turned "on" when it acquires a VEV -- are you saying that the electroweak Higgs has a nonzero VEV above the electroweak scale?

I understand that SUSY corrections affect the electroweak scale a little bit, but not by orders of magnitude. This is why I'm confused over the discussion involving GUTs, SM extensions, etc. To be clear: it's not that these extensions aren't important, but I don't think they have much to do with the electroweak scale.