## Sunday, 23 March 2014

### Weekend Plot: axing axions

Assuming the B-modes observed by BICEP2 originate from the metric field fluctuating during inflation, implications are profound. Obviously, inflationary models are now constrained to reproduce the energy scale 10^16 GeV driving the expansion (equivalently, the Hubble scale during inflation 10^14 GeV). But the consequences extend to more general new physics scenarios that a-priori have nothing to do with inflation. One prominent example is high-scale axions. Axions are hypothetical particles that pop up in many theories: as a solution to the strong-CP problem in QCD, as a dark matter candidate, as a prediction of string theory, etc. Here is a snapshot of the axion parameter space after BICEP2:

The plot shows the maximum fraction of dark matter that high-scale axions can account for versus the axion mass. If the axion scale f is larger than 10^14 GeV then the axion field can wildly fluctuate during inflation. Axion fluctuations are uncorrelated with those of the inflaton field, and give rise to the so-called isocurvature perturbations where density fluctuations in radiation and matter add up to zero. The isocurvature perturbations, in turn,  are severely constrained by Planck's CMB measurements: their power has to be less than 4% of the adiabatic perturbations produced by the inflaton field.  Hence the severe constraint on the axion: its initial displacement angle  has to be small enough as to suppress the oscillation amplitude. But the same displacement angle gives rise to the production of axion dark matter. Combining these two inputs, we learn from BICEP2 that high-scale axions alone cannot account for the observed abundance of dark matter in the universe. Moreover, even giving up on axion dark matter, one has to fine-tune the initial displacement of the axion fields to a tiny value (of order 10^-8 for f = 10^16 GeV).

Of course, like for any model that crashed after the BICEP2 announcement, Microsoft-style patches are already available. In this case, one solution is simply to take f < 10^14 GeV, that is the global symmetry whose breaking gives rise to the axion particle gets broken only after the inflation ends  (although this scenario has problems of its own). Another  possible fix is to ensure the axion acquires a large mass (>10^14 GeV) during inflation, or that the isocurvature modes were diluted by late-time entropy production. Nevertheless, high-scale axions are clearly less motivated than they were a week ago.

Erratum:
A commenter pointed out that the results in this plot disagree with other literature on the
subject. The point is that, for the axion scale larger than the Hubble scale during inflation,  the minimum displacement angle is of order H/f. For the relevant scales this always produces too much isocurvature perturbations.  Thus, the conclusions from BICEP2 are stronger than what I wrote above: high scale axions are excluded (up to the caveats in the previous paragraph) irrespectively of any assumptions about the initial displacement angle. The plot on the right visualizes the situation for the QCD axion.   The yellow region is excluded by astrophysical and CMB constraints, while the green  region  corresponds to the BICEP2 measurement of the Hubble scale during inflation. The QCD axion is now constrained to a narrow window of 10^9 ≤ f ≤ 10^11 GeV. At the top of this window it accounts for all dark matter in the universe.

Anonymous said...

I'm no expert but I'm under the impression that some of the conclusions of Marsh et. al. are in conflict with Fox et. al. in hep-th/0409059. Could you explain?

Thanks!

Jester said...

Which conclusions? At least the main message (the paragraphs in italics in Fox et al.) seems to match.

Xezlec said...

You keep mentioning 10^14 GeV, but the masses shown on this plot only go up to a value 41 orders of magnitude smaller than that. Is there a typo?

Jester said...

No. The plot shows the axion mass m which is different from the axion scale f (the scale where the global symmetry whose spontaneous breaking gives rise to a Goldstone boson - the axion). For QCD axions the two are related by m~0.01 GeV^2/f. For more general axions the mass can be considered a free parameter.

Anonymous said...

Axing of axions should direct our attention to non-axionic solutions to the strong CP problem -- that use discrete space time symmetries P and CP.

Jester said...

Only a part of the parameter space of the QCD axion is constrained by BICEP2. For 10^9 GeV < f < 10^14 GeV the QCD axion is still viable.

Robert L. Oldershaw said...

" the QCD axion is still viable."

And always will be?

Marni Dee Sheppeard said...

Are you going to comment on B-L phase transitions (with inflation or not)? Because some of these people predicted the right scale.

physicsphile said...

I was under the impression the axion DM was a nice alternative to the WIMP "miracle" as during inflation there would be different sub-Universes generated, each with different proportions of dark matter. Only those ones which had a suitably small \theta would be inhabitable as discussed in http://arxiv.org/abs/0807.1726 . I was wondering whether this new paper, you are discussing, now rules out this possibility, assuming no entropy production etc., and so makes the wimp "miracle" a more likely explanation of the DM abundance?

Anonymous said...

> Jester said...
>
>Which conclusions? At least the main message (the paragraphs in italics in Fox et al.) seems to match.

The conclusions as summarized in the abstract:

"[...] such a compact modulus can not play the role of a QCD axion and solve the strong CP problem if gravitational waves interpreted as arising from inflation with Hubble constant $H_inf \gsim 10^{13}$ GeV are observed by the PLANCK polarimetry experiment. In this case axion fluctuations generated during inflation would leave a measurable isocurvature and/or non-Gaussian imprint in the spectrum of primordial temperature fluctuations. This conclusion is independent of any assumptions about the initial axion misalignment angle, how much of the dark matter is relic axions, or possible entropy release by a late decaying particle such as the saxion; it relies only on the mild assumption that the Peccei-Quinn symmetry remains unbroken in the early universe."

Jester said...

Thanks, I see, I need to think why a small axion misalignment angle wouldn't help.

Jester said...

That's right physicsphile. A high-scale axion would generically overclose the universe, unless you fine-tune the initial displacement angle. People argued this fine-tuning could be anthropic. Up to the caveats mentioned in the next this idea is now dead: one needs much more fine-tuning of clearly non-anthropic sort to suppress the isocurvature perturbations.

Alex said...

So, with significant problems for any theory that has axions as the dominant constituent of dark matter, and with no sighting of WIMPs, let me ask this:

The new physics scale in these observations is 10^14-10^16 GeV. You've said that neutrino experiment suggest some possible physics at 10^15 GeV. With our only hints of new physics at those scales, is there any problem with a model in which dark matter's mass is ~10^14 GeV or larger? Is there any problem with a model where a bunch of the mass in the universe is composed of particles that become non-relativistic when the temperature is ~10^14 GeV?

Jester said...

It's a valid possibility. One needs to ensure these particles were never in thermal equilibrium, and then invoke a non-thermal production mechanism, but otherwise there is no problem. There are models along these lines on the market (WIMPzillas, godzillas, babyzillas, and so on).

Anonymous said...

A small initial misalignment angle wouldn't help because the axion field picks up fluctuations *around its misalignment value* during inflation (set by H_I/2 pi) in the usual way, which seed the isocurvature perturbations.

David Brown said...

Gravitons, inflatons, and axions might lead the list of undiscovered particles in free space. What might be other leading candidates?

Jester said...

Sterile neutrinos, gravitinos, neutralinos, minimalinos, anyinos, wimpzillas, babyzillas, hooperons, mini-black holes, old newspapers... it's a long list.

Jester said...

Anon, it seems you're right, Marsh et al disagrees with the rest of the literature. So the conclusion is that even fine-tuning cannot save high-scale axions. I'll put an update to the post later today.

Anonymous said...

Another way to relax the isocurvature bound on the axion CDM is to assume that the saxion (or the radial component of the PQ scalar) evolves after inflation. From Fig.1 of 1403.4186, it looks still difficult to totally get rid of the tension even if the initial position of the saxion is close to the Planck scale, though...

Sam said...

Anyone know if ADMX can be made sensitive down to axions as light as10^-4 eV?

Jester said...