## Thursday, June 26, 2014 ... /////

### Should BICEP2, Higgs have crushed the Universe?

Only if you believe that there can't be any saviors

Yo Yo and other readers were intrigued by the following cool yet slightly misleading article in the Daily Mail:

Big Bang controversy grows: Study claims universe would have collapsed 'a second after it formed' if Bicep2 results were true
Lots of science media are combining the July 2012 Higgs discovery and the March 2014 BICEP2 discovery in this apocalyptic way although some of them chose a more sensible – more correct and less catastrophic – title (I mean and praise the titles referring to "new physics"). The articles were sparked by the following paper
Electroweak Vacuum Stability in light of BICEP2 (arXiv)
by Malcolm Fairbairn and Robert Hogan from Kings College London that was published in PRL one month ago (which is why the explosion of hype right now seems to be a bit late from any point of view).

To make the story short, if both the discovery of the $125\GeV$ Higgs boson and the BICEP2 discovery of the primordial gravitational waves are valid, the Universe should have decayed – fled into an increasingly unlivable state incompatible with the particles as we know them – just a moment after the Big Bang. The following 13.8 billion years should have been impossible.

Some unusually attentive TRF readers may have noticed that the Universe hasn't collapsed yet, however. So there must be a catch, right? Indeed, there is a catch. A more accurate version of the sentence above reads as follows:
To make the story short, if both the discovery of the $125\GeV$ Higgs boson and the BICEP2 discovery of the primordial gravitational waves are valid, and if the Standard Model is everything one needs to describe all particle physics up to the huge inflation scale, the Universe should have decayed – fled into an increasingly unlivable state incompatible with the particles as we know them – just a moment after the Big Bang. The following 13.8 billion years should have been impossible.
For your convenience, let me point out that the words "and if the Standard Model is everything one needs to describe all particle physics up to the huge inflation scale" were added. Well, they make a difference, indeed! ;-)

The reason why they make a difference is that particle physics is almost certainly not described by the Standard Model that we know up to the Planck scale, so one of the assumptions (the most carefully hidden one but the least likely one!) of the catastrophic prediction almost certainly doesn't hold which makes the prediction somewhat irrelevant and unrealistic.

After all, the very inflaton field that is needed for the cosmic inflation (and that is needed for an explanation of the BICEP2 discovery) is a field outside the Standard Model of particle physics. (The "Higgs as inflaton" theories are interesting but let me neglect them here.) The minimum you have to assume to incorporate both discoveries is the Standard Model plus inflaton package but even this "slightly enriched Standard Model" is very unnatural. It's much more sensible to think that the inflaton comes in a package with other fields and particles that justify the inflaton's existence, e.g. in the Grand Unified Theory.

The particle accelerators have only seen the Standard Model particles so far but the colliding particles' energies would have to be increased 1,000,000,000,000,000 (quadrillion, although it is "just" a "biliarda" in Czech) times to reach the inflation scale. That's a lot and the assumption that they would discover nothing new in this broad range is a bit contrived.

The basic logic why the Universe should have collapsed is based on the usual ideas about the Higgs potential. Note that the Higgs boson is a single "brick" of a Higgs wave, much like the photon is a single "brick" of an electromagnetic wave. The Higgs wave is a wave on the Higgs field, much like the electromagnetic wave is a wave that makes the values of the electromagnetic field fluctuate. And the Higgs field is affected by the Higgs potential, a potential energy density that makes Nature work hard to return the Higgs field at each point of space near the "ring" where the Higgs potential is minimized:

In other words, the marble simply wants to roll down to the valley, in a random direction. It has to randomly choose the direction because they're the same a priori, and this choice is what "spontaneously breaks the symmetry". This spontaneous symmetry breaking is also what gives mass to all the massive particles, and so on. This marble-in-a-hat explanation is a more accurate version of the explanation "why the God particle gives masses to the souls" than the prevailing "explanations" involving swimming in the honey and Margaret Thatcher surrounded by journalists.

This graph of the potential energy is known as the champagne bottle bottom potential in the (capitalist) first world, as the Landau haunches in the (socialist) second world, and as the Mexican hat potential in the (poor) third world. A problem with this simple picture of the $V(h)=ah^4-bh^2$ function is that it is approximate – an effective potential for low enough energies – and the shape of this Mexican hat is changing if you focus on processes with higher characteristic energies.

This additional, slow energy-dependence is known as the "renormalization group running" and I will avoid explanations what it means in this mostly non-technical blog post. Those who know quantum field theory have surely heard about it. The big insight is that all field theories are just "effective" and they work well for some "approximate energy scale" only. To derive the effective theory relevant for a lower energy scale, one has to "run" the effective theory that was designed for a higher energy scale (or to "integrate out" the high-energy degrees of freedom in this high-scale theory) and to adjust the values of parameters in the action according to a deducible algorithm. If done properly, both effective theories will agree concerning predictions of all processes at even lower energies.

As the result of the running, the picture relevant in the inflationary era – when the typical energies and energy densities (and temperatures) were much higher than today – may look different than the picture above. In fact, it's calculable that the renormalization group running implies that the nice circle (bottom of the Mexican hat on the picture above) near the center (but away from the center) is no longer the global minimum of the exact function. Instead, there is a new minimum that is very far from the axis of the Mexican hat – either finitely far or infinitely far. Nature loves to save energy so it commands the Higgs marble to get to this new, better minimum, and the Universe over there is completely different than the Universe we know. It doesn't allow the existence of the light elementary particles we need for life, among other "details". This prediction of a crippled world is clearly wrong so there must be something wrong with the assumptions that lead to this pessimistic prophesy.

I have discussed this Higgs instability many times on this blog, e.g. in
Why a $125\GeV$ Higgs boson isn't quite compatible with the Standard Model

Higgs: living near the cliff of instability

Implications of a $125\GeV$ Higgs for SUSY

Why the Standard Model isn't the whole story
My view is that the instability is always an inconsistency and even the "not so obvious" version of the instability called "metastability" is an inconsistency that cannot be tolerated in a consistent theory because some very early cosmological processes would have probed this instability, anyway. They would turn it into the full-fledged instability.

Note that so far, we have only talked about the Higgs field. Why does it have anything to do with the BICEP2 discovery?

Well, some people, especially phenomenologists and those who are not formal theorists – people including Fairbairn and Hogan – apparently tend to treat "metastability" as a tolerable disease because it seems that we may survive in our vacuum for quite a long time even if there is a much better minimum elsewhere. However, BICEP2 – assuming it is right – shows that during inflation, the energy density was huge. It had to be huge because this huge energy density was needed to produce the gravitational waves, roughly speaking. Because the energy density was huge, the Higgs field would be "kicked" from the convenient local minimum and "forced" to probe the apocalyptic better minima that are much further from the axis of the Mexican hat.

The huge energy density that existed during the cosmic inflation, according to BICEP2, would translate any potential (meta)stability of the Higgs field to a full-fledged apocalypse.

From my viewpoint, inflation is just a very likely epoch in the childhood of our Cosmos. But even if you were imagining no inflation, there has been a very early epoch in which the energy densities simply had to be huge, so the existence of much lower-energy states always seems as a problem to me. At any rate, with the high-energy-density cosmic inflation indicated by BICEP2, it's a problem even according to people like Hogan et al.

I have actually discussed the Higgs+BICEP2 combination right after the BICEP2 announcement in March, e.g. in
BICEP2: some winners and losers
The Standard Model was identified as the #2 loser of the BICEP2 discovery – and that portion of my article is exactly the same thing that's being hyped as a cataclysm by the new Daily Mail article. I have referred to another, PLB article by Archil Kobakhidze, Alexander Spencer-Smith from January 2013 which is pretty much equivalent to the article by Fairbairn and Hogan in the more prestigious PRL journal that ignited the recent "the universe should have collapsed" wave of hype. Needless to say, there is nothing really new going on here.

OK, assume that both the Higgs discovery (sure!) and the BICEP2 discovery are real, and these arguments about the instability are right. Given the fact that the Universe is still around, what does it mean?

It means that the Standard Model isn't the whole story. I mentioned the "renormalization group running" that, among other things, causes additional changes to the Mexican hat potential for the Higgs field as a function of energy. An important fact is that this Mexican hat is being changed in a way that depends on the composition and properties of all particles in your theory of particle physics, especially those that strongly interact with the Higgs – because we're looking at their effects on the Higgs potential, and some interactions of those other particles with the Higgs (some "Feynman vertices") are needed for them to cause such a "renormalization group running" change of the Mexican hat.

Some hypothetical particles apparently have the capacity to change the character of the change of the Mexican hat potential for the Higgs field as the function of energy. If you want to have a good enough mathematical model, imagine that the exact potential also has the term $ch^6$ and we need $c$ to stay positive for the potential to be bounded from below. However, the Standard Model is trying to send $c(E)$ to $c(E)\lt 0$ as we are increasing $E$ from the LHC scale to the inflation scale; additional particles and effects – saviors – are needed to slow down this decrease of $c$ and to protect the positivity of $c$ – well, the positivity of the quartic coefficient itself is a threat, too. Which particles are the Messiahs that will save us?

It may be seen that the promising enough saviors may be both bosons or fermions. If they're fermions, they must be extremely similar to the "higgsinos", spin-1/2 superpartners of the Higgs boson in supersymmetric theories. If they are bosons, they must be extremely similar to "top squarks" or "stops", the supersymmetric partners of the top quark. In all discussions about the Higgs things, the top quark is the most important quark because it's the heaviest one – and because the mass is proportional to the strength of the quark's (or lepton's) interactions with the Higgs field. The effect of other, much lighter quarks and squarks on the Higgs field is negligible in comparison.

The Higgs field has strong interactions with itself (self-interactions) which, via supersymmetry, also implies strong interactions with its superpartner, the higgsino, and those interactions with the (so far unobserved) higgsinos are also important enough to modify the running of the Mexican hat potential and to avoid the catastrophe.

(Numerically, the stops are probably more important for the salvation, like Jesus Christ. The higgsinos are only as important as the Holy Spirit.)

So if you want the Universe to be saved, you should pray for the coming of particular saviors which are either higgsinos and stops from a supersymmetric theory, or someone who looks almost just like them. You see that I describe the saviors in such a way that they make supersymmetry "almost inevitable". Supersymmetry isn't quite inevitable and you may imagine that the relevant new particles that save our Universe from the "collapse" are particles unrelated to supersymmetry, in a world that perhaps isn't supersymmetric.

The (not quite lethal but still noticeable) problem with these non-supersymmetric explanations and non-supersymmetric particles is that they apparently need to "imitate" the stops and higgsinos from the supersymmetric theories, and there exists no other justification – a justification different from supersymmetry as a principle of Nature – that would justify the existence of particles that seem to pretend that they are supersymmetric partners even though they fundamentally aren't.

(If you are a hardcore anthropic principle believer, you may treat the ability of a new particle to "save the life" to be its only feature that matters, and from this viewpoint, you probably don't care a single bit whether the new particle follows from some sensible, justified, and pretty principles such as supersymmetry or it is a random piece of stinky trash. Clearly, I am no hardcore anthropic believer.)

Using the Jesus Christ metaphor, the simultaneous validity of the Higgs and BICEP2 discoveries along with the self-evident long survival of our Universe would imply that our Universe was saved either by Jesus Christ – by the supersymmetry and especially the two new particles it predicts (higgsinos and stops) – or by a false prophet pretending to be Jesus Christ even though he is fundamentally someone else. You are free to pick your preferred explanation of the salvation among the two.

(Note that it was hard to choose the right capitalization of "He"/"he" in the case of Jesus Christ and the false prophets. There are isomorphic subtleties involving the "H"/"h" in the case of the Higgs boson and higgsinos.)

It is a question where we don't have any rock-solid proof in one way or another but I choose the real Messiah, someone who is a savior because of His or Her intrinsic properties and not because of some random adjustments – namely supersymmetry. Lots of other new physics may stabilize the Higgs potential but much of new physics is likely to be useless for the stabilization and the number of new particles in the LHC-to-inflation range that are helpful is probably rather small and SUSY is probably the main if not only thing that matters.

#### snail feedback (20) :

Hi Lubos,
A question for you regarding these vacuum instability discussions - it looks like people have calculated the effective potential (i.e. the part of the 1PI effective action that doesn't depend on field gradients) using RG methods and found that \phi=0 is not the global minimum for certain values of parameters. But does this really mean an instability? Aren't the bubble nucleation calculations for decay of the false vacuum done using the bare action (the one that appears in the path integral)? The 1PI effective action is what you get after you've already done the path integral completely, so it seems nonsensical to use it to talk about vacuum decay.

Dear Guest, just for potential other readers, metastability means that there is a lower global minimum, but one may only get there by tunneling - which may be potentially very unlikely, slow, and therefore "safe and tolerable".

Concerning your question, you may always do your calculation using the bare action but you must correctly incorporate all the quantum corrections - loop processes, instantons, and loop corrections on top of instantons, whatever matters. The usage of the effective actions in the calculation of the ultimate fate of the Universe - which you may interpret as an extremely low-energy question - is supposed to simplify this calculation so that some/all loop corrections are added from the beginning and the resulting instanton calculation may be done pretty much classically.

One must still be careful whether a given calculation incorporates all the quantum corrections that it should. I think that what you're imagining as the decaying instanton calculation clearly doesn't incorporate everything it should. You didn't use formulae but your words suggest that you think that such questions may be decided by a purely classical calculation. They never can't. Quantum mechanics always matters and whenever it may be approximated by classical physics for some class of questions, you must use the appropriate effective actions.

I think that it's useless to spend too much time with these details because at these high energy densities and large values of fields, field theory is almost certainly at least marginally inapplicable and one needs a full calculation in quantum gravity or string theory.

Hey Lubos. Wanna earn $10 000? http://www.theblaze.com/stories/2014/06/25/want-to-disprove-man-made-climate-change-a-scientist-will-give-you-10000-if-you-can/comment-page-3/ reader Albert Zotkin said... Acording to Martinus J. G. Veltman if the Higgs boson existed then the size of the universe would match that of a bustard egg. As you can see here the bustard eggshell is actually a CMB radiation map http://tardigrados.files.wordpress.com/2012/10/wmap-egg1.jpg?w=760&h=509 ;) reader OXO147 said... That's$10k, plus \$15k for the Fields Medal if you can figure out how prove a negative.

"...published in PRL one month ago (which is why the explosion of hype right now seems to be a bit late from any point of view)."

I conjecture that this observed delay is explainable by the typical speed of thinking of an average science journalist or editor ... ;-P

As I previously said, this crook will never pay a penny to anyone even though, according to his words, he should. There is nothing that forces crooks of this kind to fulfill their promises.

What is does it a pure propaganda gesture. Could people please stop discussing this non-event?

Hi Lubos,
Indeed, the subject of vacuum destabilization by inflation is relatively old : http://arxiv.or/abs/arXiv:0710.2484
There is not much more one can say.

One thing I should mention is that people usually forget about the coupling between the Higgs and inflaton. It should be there because it's renormalizable, gauge and Lorentz invariant, so by QFT rules one should include it. And it is this coupling (even if it's very small) that can solve the problems with stability in the absence of any new physics up to the string scale (search for 'metastable vacuum and inflation').

Privět!

The 2007 paper indeed said enough. Hard to see what the supposed progress afterwards has been.

Could you please give me specific papers discussing the Higgs-inflaton coupling?

E.g. arXiv:1210.6987
The result is that if the coupling is positive (which could be as small as 10^⁻6 and less), the problems are solved.

The Big Bang vacuum was intensely chiral. It intrinsically resisted collapse. Pseudoscalar field decay-powered cosmic inflation, smoothing it to apparent isotropy. A trace chiral vacuum background remains. Five matter-based tests measure that chiral vacuum remnant They originate external to physics, immune to its defective postulate.

One skimmed de Laval vacuum supersonic expansion nozzle, one pulsed chirped FT μwave spectrometer; a vacuum pump, a tank of helium, a few grams of racemic D_3-trishomocubanone. One day measuring divergent enantiomorphic molecular rotation temperatures. Confirm with a 90-day geometric Eötvös experiment.

Go , Lubos, go :).

For me your analysis is clear :taking both as true, Higgs and BICEP2 is a new experimental observation that implies new physics over the standard model, Almost as good as finding experimentally a magnetic monopole :)

yup I think I can see the CMB cold spot 8)

Nice review. A question for clarification. If I understand, a and b are well (?) determined at current energies. By RG can they also run with energy? Also is there any experimental indication of non zero c at current energies?

Hi Kashyap, one function of a,b - the vacuum expectation value 246 GeV - has been known from the W,Z masses for decadees. The other independent function needed to determine both a,b has been known since the Higgs mass was measured to be 125 GeV.

The other coefficients like "c" are classically zero because the theory would be nonrenormalizable but the exact quartic profile is just a classical approximation and quantum mechanically, there are lots of corrections to the shape. I summarized them as the sixth order term but this is not the most accurate description of the quantum corrections to the shape, e.g. some functions with logarithms in them.

Yes, all constants like a,b as well "c" (this literal one as well as its more relevant, generalizations) are RG running i.e. energy-scale-dependent.

Thanks Lubos. Then, if the change is also logarithmic, it will take huge change in energy to make substantial change in a,b,c. Of course in principle you are talking about 10^19 Gev or more! Is this right?

The Higgs-Inflaton coupling is discussed in the paper (and the below mentioned paper is cited)

Is your cryptic suggestion related to the right hand rule chirality of the fixed direction of induced current when a magnet is moved through a metal ring? This is an everyday already established chirality is it not? I am still looking for a Motl worthy write up about it since Wikipedia seems too bored with it.

Massless boson photons detect no vacuum refraction, dispersion, dissipation, dichroism, gyrotropy. Postulate this is exactly true for fermionic matter (quarks). Parity violations, symmetry breakings, chiral anomalies, baryogenesis, Chern-Simons repair of Einstein-Hilbert action suggest vacuum trace chiral anisotropy acting only upon hadrons is being observed. LOOK to validate or falsify: geometric Eötvös experiment, geometric enthalpies of fusion[1], geometric microwave rotation temperature[2], geometric pawnbroker rotation, geometric Galilean drop[3].

[1] http://www.mazepath.com/uncleal/shoes2.png

[2] H. K. Moffat, Six lectures on general fluid dynamics and two on hydromagnetic dynamo theory, in R. Balian & J-L Peube (eds), Fluid Dynamics (Gordon and Breach, 1977)