Does electroweak symmetry breaking involve quantum tunneling?
I don't think so. I believe the typical belief is that electroweak symmetry breaking was a thermal phenomenon: at high temperatures, the electromagnetic and weak forces behaved as one force. As the temperature lowered, self-interactions caused the field to settle in a state that was a local minimum of energy (possibly global, but not likely).
Tunneling would be involved if the field tunneled from that local minimum to another, nearby local minimum. I don't think there's any evidence that something like that happened related to electroweak symmetry breaking. Tunneling may have played a part in the early universe (it's often brought up in the context of inflation), but I don't think it played a part here.
Any possible similarity of electroweak symmetry breaking with inflation and GUT symmetry breaking involving tunneling was indeed what I was trying to ascertain - especially regarding whether the Mexican hat represention of GUT energy density roll down can also be applied to electroweak symmetry breaking.
Electroweak symmetry breaking would be more accurately described as a phase transition than tunnelling as Chalnoth pointed out above. Timing is a bit tricky and heavily model dependant as to which dynamics occurs and when but usually the older models such as False vacuum had the tunnelling occurring prior to electroweak symmetry break as far as I know. Though extremely close together lol.
I don't if this is a golden rule but I've noticed anytime your dealing with inflation your under scalar field modelling ie quantum tunnelling . Once you symmetry break you now have additional fields so you have to account for these additional degrees of freedom. This where I tend to see described under nucleosynthesis via Bose-Einstein and Fermi-Dirac statistics. I don't recall ever seeing tunnelling described after electroweak symmetry break. Except in bubble universe models
In other words, phase transition can occur either with tunneling, as in GUT symmetry breaking, or without tunneling mechanism, as in electroweak symmetry breaking.
Well electroweak symmetry break certainly doesn't require tunneling it just requires an expanded volume and rate of expansion sufficient to allow the required particles to decouple from thermal equilibrium. I've never seen this described via tunnelling. Been awhile since I looked at the break itself but the timing involves the fields coupling constant. As temperature rises the coupling constants gain in strength and become essentially indistinguishable if I recall correctly the term "Running of the coupling constants" was used to describe this at one time.
Muchanovs Fundamentals of Cosmology has excellence coverage on this so I can check that later for you
Ok, clear. Thanks to both.
Why do you think GUT symmetry breaking requires tunneling?
Here this will help understand electroweak symmetry break via GUT theory
http://arxiv.org/pdf/0904.1556.pdf The Algebra of Grand Unified Theories John Baez and John Huerta
http://pdg.lbl.gov/2011/reviews/rpp2011-rev-guts.pdf GRAND UNIFIED THEORIES
It covers SO (10) as well.
nucleosynthesis is detailed in chapters 3 snd 4 here
http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodyna
We went through this in his other thread on this. He's been told it doesn't.
'Slow roll' phase transition of inflation, preceding GUT symmetry breaking is described by a flattened Mexican hat energy density representation. Can electroweak phase transition be also described by a flattened Mexican hat energy density representation?
In the simplest version, "slow roll", AFAIK, doesn't even use a Mexican hat potential; just a one-dimensional potential with a "hill". Note that there is no tunneling required.
I am not aware that this "slow roll" transition is also the same one that precipitates GUT symmetry breaking. Nor am I aware that GUT symmetry breaking is currently modeled using such a potential.
As far as I know this is the currently favored model, yes.
"I am not aware that this "slow roll" transition is also the same one that precipitates GUT symmetry breaking. Nor am I aware that GUT symmetry breaking is currently modeled using such a potential"
Not sure on this but there is a correlation to the seesaw mechanism of Higg's inflation but the stages I'm thinking of is under supersymmetry SO (10) MSSM. It gets a little tricky to follow to answer accurately. Which is why I'm hesitant as it also depends on which SU break the OP is considering as the GUT break which can vary depending if hes only considering the Glamshow or including Pati-Salam including Higgs for the minimal SM SO (10) which I've ever seen one paper on. SO (10)MSSM is incredibly easy to find but SO (10) MSM incredibly impossible.
Though I will admit there is aspects of the Higgs field I am still studying which includes the seesaw mechanism which at one time I thought I understood but a dissertation paper I picked up made me realize there was aspects I had wrong.
I've literally lost count of the number of seesaw variations I've come across on arxiv. seesaw 1 seesaw 2 seesaw 3. with variations on each.
Here is an arxiv that discusses GUT and refers to the seesaw mechanism. As I stated I'm unclear on various aspects of it
apologize for the Google link my phone tends to autodownload.
As far as Higg's inflation the Encyclopedia Inflationaris (ASPIC Library) still considers this a viable inflation model. They regularly test the numerous inflation models to the available datasets ie Planck.
As to the dissertation I've been studying its
"Higg's dynamics during Inflation" by Stephen Stophyra. Its strictly done in the standard model regime
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