Is Higgs Inflation Still Viable After Moriond and Planck Data?

[nikkkom]

Is it possible that Higgs vev and cosmological constant are linked?

Imagine that in the inflation era, Higgs field was in another trough of stability, with much higher vev. Thus cosmological constant was big too (hence, inflation).

When (or where) Higgs field tunnels into currently observable vacuum state with small vev, cosmological constant becomes very small and inflation stops.

 

[haushofer]

Can someone perhaps recommend a nice pedagogical introduction into the concepts of Higgs-inflation (with prerequisites being QFT and cosmology)?

 

[nikkkom]

"Investigating the near-criticality of the Higgs boson", section 5.3 - Higgs and top couplings are said to both be near-critical. This is a fact of broad general interest. It could indicate landscape statistics, anthropic tuning, Planck-scale physics...

I have doubts that our current vacuum can be metastable.
If there is another vacuum state with lower energy, it may be difficult to tunnel into now, in low-energy era (thus, metastability).
But in early Big Bang average energy density was much higher. If there was an era when average energy was higher than the barrier between two vacuums, Universe would certainly settle into the vacuum with lower energy.

Thus, either our vacuum is the stable one, or the barrier between vacuums is higher than maximum energy ever attained during Big Bang. Hmm. So the metastability of the vacuum implies that Big Bang had no singularity, it had a maximum in enegry.

 

[mitchell porter]

Another paper today on Higgs monopoles, by an author of the paper mentioned in comment #23. It would be neat if they could account for dark matter.

Which reminds me, back in November, the discussion of Higgs vev and cosmological constant led me to the work of Fred Jegerlehner, which may be the apotheosis of trying to explain beyond-standard-model physics using the Higgs. Not only does he advocate Higgs inflation, but he tries to get the c.c. from the Higgs vev, and even tries to get baryogenesis from the Higgs. I don't have time to dig through his work again, but I think for baryogenesis, his idea is that the Higgs field has another minimum in which the excitations are superheavy, and the baryon asymmetry is created in the very early universe when those superheavy Higgs bosons are in the mix. As for the c.c., I don't remember the logic at all, but I think it had something to do with his particular philosophy of Planck-scale physics; a sort of finetuning argument, but not anthropic. I really don't remember...

... and I also don't believe any of it. I had wanted to post about it (and to respond to the latest comments) back in November, but I wanted to first get clear on why I didn't believe it, ran out of time, and then forgot about it. I can at least state a philosophy. I'm very sympathetic to people who think the standard model is very elegant - compared to the endless stream of grand super brane models produced during the last 40 years, with all their completely unobserved features - and who would like to see everything that remains to be explained, explained by some simple new ingredient, that would serve as a capstone to the standard model and give us an even more elegant theory of everything. I suspect that the truth is elegant, and even simple in some way, but that it will also have the mathematical depth of M-theory. So I look with apriori skepticism upon the minimalists who argue that there are easy overlooked answers, like Jegerlehner.

But that's all just blah blah, compared to actual rigorous reasoning and calculation, as a response to Jegerlehner's specific claims; something I can't provide, unfortunately. But perhaps someone else can.

 

[mitchell porter]

"Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity". The Higgs-Yukawa model consists of fermions, a Higgs field, and yukawa couplings between them. It's like the standard model without the gauge fields, and can be used to study the running of the top quark and the Higgs, the key players in the criticality of the Higgs mass. This paper studies how well the asymptotic safety (AS) approach to Higgs criticality coexists with Higgs inflation, and discovers a problem: the special coupling between the Higgs field and the Ricci curvature scalar, that is at the heart of Higgs inflation, becomes "irrelevant" at the AS fixed point. The immediate meaning of this is that this coupling is not a free parameter of the theory; the free parameters are the coefficients of the "relevant operators".

The authors write as if this finding falsifies this version of Higgs inflation. But doesn't it just mean that the Higgs-Ricci coupling ζ is going to be a prediction, rather than a free parameter? The authors note (top of page 4) that Higgs inflation, for a critical Higgs, can work with quite a small value of ζ; one might view this as improving the model's prospects... I should also note that for the simpler case where there's just a Higgs, and no fermions, ζ is relevant and therefore a tunable parameter. It's possible that this is also true for the full standard model, or some extension of it. Further calculation is required.

But what intrigues me most is the possibility that there is a connection between Higgs criticality and finetuning of Higgs inflation, and that for some reason the unknown UV physics actually determines that the Higgs-Ricci coupling is appropriately tuned.

 

[fzero]

The authors write as if this finding falsifies this version of Higgs inflation. But doesn't it just mean that the Higgs-Ricci coupling ζ is going to be a prediction, rather than a free parameter? The authors note (top of page 4) that Higgs inflation, for a critical Higgs, can work with quite a small value of ζ; one might view this as improving the model's prospects... I should also note that for the simpler case where there's just a Higgs, and no fermions, ζ is relevant and therefore a tunable parameter. It's possible that this is also true for the full standard model, or some extension of it. Further calculation is required.

But what intrigues me most is the possibility that there is a connection between Higgs criticality and finetuning of Higgs inflation, and that for some reason the unknown UV physics actually determines that the Higgs-Ricci coupling is appropriately tuned.

I can explain a bit of the generalities of RG flows that are assumed by their discussion and not explicitly spelled out. Let's say we have some conformal fixed point. Usually we think of the fixed point as an explicit point in the coupling constant space of the theory. If we have a Lagrangian description of the theory, then we could specify an action $S$ at the fixed point. In addition we would have a collection of local operators $\mathcal{O}_i$ constructed from the fields in the theory. Usually the RG flows are generated by deforming the theory by adding a local operator to the action, resulting in a new theory
$$S' = S + \int g_i \mathcal{O}_i.$$

The RG equations will tell us how the parameters $g_i$ transform with the scale. The resulting trajectory in the coupling constant space is called the RG flow. The place to start is for infinitesimal $g_i$, so we start in a small neighborhood of the fixed point and the RG equations will specify critical exponents for the scale dependence. We also need to have these flows start in a small neighborhood if we want to discuss flows that are smoothly connected to the fixed point. This leads to the picture of critical surfaces as discussed in the paper.

The deformation above will generate a one-dimensional flow, where, of course, we are always flowing from the UV to the IR. For an irrelevant deformation, the coupling constant is getting smaller as we flow to the IR, so the theory is actually returning to the fixed point, with $g_i=0$ . Conversely, for a relevant deformation, the coupling constant grows as we move to longer scales, so we get a new theory.

If we consider a two-dimensional deformation by adding both an relevant and irrelevant deformation, $g_r \mathcal{R} + g_i \mathcal{I}$, then we can think of the local geometry of the fixed point in the following way. We have axes for the coupling constants $(g_r,g_i)$ with the fixed point at the origin and we consider the quadrant between the axes (since we'll ignore the actual sign of the coupling constants). The RG equations kind of dictate a "potential energy" function (in 2d this would be the $c$-function) that pushes the flows. In the irrelevant direction $g_i$, this potential function is increasing, so we are pushed back to the origin. In the $g_r$ direction, the function is decreasing and some RG flow is allowed. In between, the function must be sloping down from the $g_i$ axis to the $g_r$ axis, so at least for small deformations, the flow from a given point $(g_r,g_i)$ is to a point $(g_r',0)$ and then further flows will take place along the $g_r$ axis.

So what the paper is saying is that the theories in the IR with nonzero nonminimal coupling cannot be smoothly connected to the UV fixed point.