Higgs field

[Brainee]

What is in a Higgs field/energy bowl?

[Mordred]

20 minutes ago, Brainee said:

What is in a Higgs field/energy bowl?

The bowl your referring to is the potential energy levels that correspond to the vacuum expectation value 

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

equation 2 on this link in a plot lloks like this without the full 3d rotation

https://www.wolframalpha.com/input?i=plot+V(\phi)%3D-5|\phi|^2%2B|\phi|^4

 

the high point is called the false vacuum potential prior to electroweak symmetry breaking. As the potential rolls from the top point to the potential at the bottom either left or right lower this is the current Vacuum expectation value of 246g GeV today that gives rise to the mass term. It is a potential energy graph so nothing is within it 

[Brainee]

Thanks for answer. I do not  really understand what Higgs field/energy bowl is?

[Mordred]

which term didn't you understand

Field: as set of values under a geometric treatment. 

energy; the ability to perform work

potential energy the energy (ability to perform work) due to location. (geometry) example gravitational potential energy at sea level vs top of Mt Everest

the graph I posted is the potential energy and how it evolves prior to electroweak symmetry breaking and after electroweak symmetry breaking. Prior to electroweak symmetry breaking elementary particles did not have mass. After symmetry breaking leptons and neutrinos gain mass due to the Higgs field potential.

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

perhaps this might help its a very straightforward FAG by Professor Matt Strassler

https://profmattstrassler.com/articles-and-posts/the-higgs-particle/the-higgs-faq-2-0/

 

 

Edited January 2, 2023 by Mordred

[MigL]

Since this hasn't gone any farther, maybe I can pose a question or two.

If we consider the 'sombrero' potential, and the roll from the centre peak of the hat down into the brim ( false vacuum to true vacuum potential ), to account for the inflationary epoch, as a result of the symmmetry break when the Electroweak dissociated, to what do we attribute the 'rate' of the roll-down ?
Did the 'roll' stop when inflation ended, or did it slow down, and continues to account for expansion ?
IOW, have reached the true vacuum potential yet or are we still very slowly working towards it ?

Further, if you make a real world model of the sombrero potential and use a marble as the universe's potential, you find that the marble oscillates across the brim, before coming to a complete stop at the lowest point.
Could the same oscillations be occurring to the universe's potential, and account for periods of increased and decreased expabion rates ?
Or, am I reading too much into the model ?

Edited January 3, 2023 by MigL

[Genady]

16 minutes ago, MigL said:

if you make a real world model of the sombrero potential and use a marble as the universe's potential, you find that the marble oscillates across the brim, before coming to a complete stop at the lowest point.

However, if we model moving down the potential by a cooling body, nothing like that happens.

[MigL]

True.
However the universe is an expanding cooling 'body'.

The mable has inertia which is affected by gravity, causing the oscillations.
Could the universe have the same ?

[Genady]

14 minutes ago, MigL said:

The mable has inertia which is affected by gravity, causing the oscillations

plus there is a friction to slow it and to make it stop at the lowest point. Where would the "inertia" and the "friction" come from?

[Brainee]

Is it particles like electrons that move in Higgs field?

[swansont]

1 minute ago, Brainee said:

Is it particles like electrons that move in Higgs field?

AFAIK the Higgs field is everywhere, so all particles move in the field.

[Mordred]

2 hours ago, MigL said:

Since this hasn't gone any farther, maybe I can pose a question or two.

If we consider the 'sombrero' potential, and the roll from the centre peak of the hat down into the brim ( false vacuum to true vacuum potential ), to account for the inflationary epoch, as a result of the symmmetry break when the Electroweak dissociated, to what do we attribute the 'rate' of the roll-down ?
Did the 'roll' stop when inflation ended, or did it slow down, and continues to account for expansion ?
IOW, have reached the true vacuum potential yet or are we still very slowly working towards it ?

Further, if you make a real world model of the sombrero potential and use a marble as the universe's potential, you find that the marble oscillates across the brim, before coming to a complete stop at the lowest point.
Could the same oscillations be occurring to the universe's potential, and account for periods of increased and decreased expabion rates ?
Or, am I reading too much into the model ?

Ok I do have tchnically 2 threads ongoing with the related mathematics of Higgs inflation.

 https://www.scienceforums.net/topic/128412-musings-of-a-mad-scientist-inflation-as-cosmological-constant/

the first part is just the FLRW metric as I needed to get the equations of state for comparison for a single scalar Higgs field. The second part details the standard Higgs inflation mathematics.

I'm still working on this part in greater detail in this thread I have in speculation but its rather random as I research each portion.

https://www.scienceforums.net/topic/128332-early-universe-nucleosynthesis/

anyways if the Higgs inflation is correct and for the record the equations of state are identical to the standard inflaton field. A quick run down is as follows, the initial hot dense state had an extremely high kinetic energy term that when applied to the equations of state exceeded the critical density at that time. As the kinetic energy exceeded the potential energy by such an extreme expansion is a consequence to begin with. So your maximal false state is roughly 

 \[10^{16\rightarrow..19^2}.. GeV\]

 As the expansion is already underway, you get the subsequent cooling (the slow roll stage) quark gluon plasma state where all particles are still in thermal equilibrium. At the volume curvature is still meaningless and in that thermal equilibrium state the effective degrees of freedom is a mere 2... hence the low entropy beginning. The two degrees of freedom is the polarities of the photon.  As the effective degrees of freedom re the result of temperature with the photon as the mediator. At this stage you apply the Goldstone bosons correlations to the Higg's field. (invariant massless field). The consequence of the expansion allowed a sufficient drop in temperature (you an apply the photon redshift relations to the cosmological redshift formula) for a rough estimate Symmetry breaking occurs, this correlates with the rapid descent of the Sombrero hat. (number of e-folds in excess of 60 to fit observational data. The result of the rapid expansion leads to supercooling. 

Now this stage is important to understand prior to inflation the universe curvature didn't particularly matter due to the small volume in essence. However inflation of 60 e-folds later left a very close to critical density so k=0, approximate. the effective equation of state is the ultra relativistic radiation. The supercooling and critical density value both apply to the slow roll stage. Inclusive in this is the addition of a mass term to the particle species that have dropped out of thermal equilibrium. The "Friction is a correlation to that additional mass term". 

 Another important detail is the transition from the false vacuum state to the true vacuum state need not be smooth you can have numerous other  semi states and still match observational data. This detail likely be the result of various particle species decoupling, the result of each decoupling alters the effective expansion rate.

quote from above

Further, if you make a real world model of the sombrero potential and use a marble as the universe's potential, you find that the marble oscillates across the brim, before coming to a complete stop at the lowest point.
Could the same oscillations be occurring to the universe's potential, and account for periods of increased and decreased expansion rates ?
Or, am I reading too much into the model ?

Not really due to the equations of state for radiation relation to the Hubble volume which relates to how the E-folds are calculated.  If the kinetic energy term can exceed to Hubble radius in a given short time frame as defined by the E-fold logarithmic function quickly decreases but as it stabilizes it essentially merges with the radiation equation of state rather it becomes dominates by the radiation equation of state

we do not know if were currently at minimal there is some conjecture we may also be in a semi stable stage.

 

 

Edited January 4, 2023 by Mordred

[Brainee]

Thanks a lot for answers.

Simplified when does particle roll in Higgs field? How is it today compared to earlier times?

[Mordred]

The initial roll depends on the model which has some variations but roughly 10^{-32} seconds after the big bang. Don't think of it as a particle rolling downhill that would be incorrect. Instead think of it as the potential energy density of the early universe decreases. Today we may or may not be in a metastable state but at lower potential. or we could be close to the minimum. There are competing models on this.