Higg's field thermodynamic research CMB and now

[Mordred]

The intention of this post is not a speculation, its an ideal I wish to test out. So I don't want replies based on speculation or personal theories.

 

Now here is the Cosmic inventory

 

http://arxiv.org/pdf/astro-ph/0406095v2.pdf "The Cosmic energy inventory"

 

The one value missing from this inventory is the energy contribution of the Higg's field itself.

 

So I wish to use the Bose-Einstein statistics, based on the only confirmed Higg's Boson we have confirmed (reasonably). As the Higg's particle is a boson this statistic should work, for fermions we use the fermi-dirac statistics.

 

The purpose of this research is to see if I can further constrain the cosmological constant itself. (possibly) The two time periods I will examine is via the temperature of the CMB and the temperature of the universe today

 

 

However I have a couple of questions.

 

1) first does anyone know of a reason why the Bose-Einstein statistics cannot be used in this case, if not what statistic is more appropriate ?

2) The cosmological constant is a positive energy, with a negative pressure contribution determined by its equation of state. Has anyone come across or seen an equation of state relating to the 126 GeV Higg's. (or knows if it is a positive or negative pressure contributor) (I would assume the Higg's field EoS may be the same as the relativistic radiation, however thats an assumption)(may be more appropriate to use the scalar field EoS, though via the standard model the vacuum expectation value is 246 Gev considerably less than the CMB)

 

any professional peer review papers are welcome in terms of the thermodynamic properties of the Higg's itself are welcome.

Edited June 17, 2014 by Mordred

[beefpatty]

1) B-E should be correct; have you read otherwise or are you just making sure?

2)The scalar field eq. of state would be appropriate, which I write here for convenience (in the perfect fluid approximation): [math]w = \frac{\frac{1}{2}\dot{\phi}^2 - V(\phi)}{\frac{1}{2}\dot{\phi}^2 + V(\phi)} .[/math]

 

You can see that for [math]w = -1[/math] you need a vanishingly small kinetic term for the region you are interested in. For the Higgs field this can be achieved either through a non-minimal coupling of the Higgs field to gravity http://arxiv.org/abs/0710.3755 or with a non-minimal coupling in its kinetic term http://arxiv.org/abs/1006.2801. The previous two papers work to identify the Higgs field as the inflaton, however.

 

Why do you need B-E statistics, though? The Higgs field may contribute to dark energy, but its VEV is much too large and would either have to elegantly cancel with other VEV's or should be finely tuned. Lawrence Krauss wrote a paper trying to connect the Higgs and dark energy (unfortunately it is behind a paywall but you can read the abstract here.) Here is also another paper, which I admittedly did not read as it is rather lengthy at 39 pages.

Edited June 17, 2014 by beefpatty

[Mordred]

Thanks Beefpatty, just making sure I couldn't think of any reason why the B-E wouldn't be appropriate. Much like the papers you have posted the only examples I've usually read deals with the Higg's in terms of its TeV metastabiltiy above 10¹¹ GeV. I have easily been able to find papers dealing with the Higg's at high temperature ranges. SO(10) papers have numerous examples and relies on the Higg's for the seesaw 1 and seesaw II mechanism. However I've yet to find any papers covering the Higg's below the standard model 246 VEV.

 

So I'm not looking at the Higg's mechanism itself but rather the Higg's bosons contributions (if any) to the thermodynamics after spontaneous symmetry breaking. Which is where I'm hoping the B-E can be used to give an approximation of the energy density and pressure contributions below the VeV. (I've never read or seen any papers covering Higg's below the 246 VeV, so I'm not sure if there is any further contributions below that range in terms of thermodynamics, the fact I never see any papers dealing with the Higg's interactions temperatures of the universe from the CMB to today) makes me wonder if there is or isn't an influence in current times cosmology.

 

Why do you need B-E statistics, though? The Higgs field may contribute to dark energy, but its VEV is much too large and would either have to elegantly cancel with other VEV's or should be finely tuned. Lawrence Krauss wrote a paper trying to connect the Higgs and dark energy (unfortunately it is behind a paywall but you can read the abstract here.) Here is also another paper, which I admittedly did not read as it is rather lengthy at 39 pages.

 

I'll have to see if I can locate a copy of the paper by Krauss, thanks for these. This is specifically what I am looking for (currently studying the 39 page article)

 

lol at least I'm not the only one that had that idea

 

just glancing over the 39 page paper it looks like it has the information I was curious about including the related formulas much thanks for that

 

"What is at our disposal is essentially only the value of the Higgs field at the Planck scale, since in the experimentally
accessible low energy region the Higgs field is not an observable and we only know its vacuum expectation value."

 

this statement explains, why finding papers covering current influence is so tricky. awesome paper lol (my apologies if I'm acting like a kid with a new toy hehe)

Edited June 17, 2014 by Mordred

[beefpatty]

No problem! After looking more carefully it seems the second paper (by Jegerlehner) is rather interesting and probably what you are looking for. I should probably study it more .

I think it is rather interesting because it only requires SM physics to account for inflation and a small cosmological constant both from the Higgs.

 

Do you mind if I ask if you are a graduate student in Physics, an amateur, or perhaps even a full-blown researcher?

 

Edit: He also appears to have some talks related to this on this website: http://www-com.physik.hu-berlin.de/~fjeger/

Edited June 18, 2014 by beefpatty

[Mordred]

The reasons you mentioned is precisely why I like the article, lets just say I'm a very well studied long term amateur. In that I've been studying physics for over 20 years. As well as buying and studying a huge collection of the textbooks, however I've never taken institutional training. Luckily though I do have a few professors in the field that I personally know that help me along. (as well as correct my mistakes lol) they have even had me do some of their exams. My actual stock and trade is an Industrial electronics controls tech. In other words design, program and repair robotics and automated systems. (requires a high degree of mathematics, makes understanding physics easier).. If you ever watched "How its made" I design and repair the equipment that makes those items

 

needless to say cosmology has come a long ways in the past 20 years, I recall arguments on whether the universe was flat,curved etc before LCDM became strong and the WMAP data.(it was funny as people were trying to invent their own shapes and show the metrics for it) The MOND vs quintessence,vs BB,string debates were also amusing. That was when Space.com used to have a forum

 

Another related paper Fred Jegerlehner wrote

 

http://arxiv.org/abs/1406.3658

"About the role of the Higgs boson in the evolution of the early universe"

 

related by different author

Multifield Dynamics of Higgs Inflation

http://arxiv.org/abs/1210.8190

Edited June 18, 2014 by Mordred

[beefpatty]

I see you are quite passionate then. I myself am a second year grad student doing research in inflation, so I find all of these topics interesting.

Thanks for the other papers!

[Mordred]

Inflation is a good area of research, One of the professors I know from another forum (though not personally) is also researching inflation

 

here is his papers

http://arxiv.org/find/all/1/all:+AND+Brian+Powell/0/1/0/all/0/1

 

he has given me permission to place one of his articles on my website see signature

http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell (written for laymen hehe, he got tired of the same questions on the other forum lol)

you should also have a copy of this if you haven't already, they regularly test various inflation models its 365 pages long so use it as a reference

 

Encyclopaedia Inflationaris

http://arxiv.org/abs/1303.3787

 

"ASPIC already has 74 different inflationary scenarios, a number that should be compared to the three or four models that are usually consi
dered. The ASPIC library is an open source evolutive project and, although it already contains all the most popular
inflationary scenarios, aims at including more models"

Edited June 18, 2014 by Mordred