Tuesday, 1 April 2014

Higgs Inflation Flexes its BICEPs

A couple of weeks ago we had the BICEP2 announcement, a new and exciting physics result that was perfectly timed with my parents visiting.  As such I rather missed my chance to comment at the time, and with inflation being somewhat beyond my area of expertise I wasn't sure I really had much to say that was better than, for example, Resonaances.

However, one thing that did strike me from that post was the following line:
Speaking about model building, Higgs inflation is ruled out, at least in the current version. A robust prediction of Higgs inflation is no tensor modes at an observable level. In other words, we have a new evidence for new physics beyond the Standard Model. 
If I've learnt anything in my time as a postdoc, it's that whenever you make this kind of statement it's just a matter of time before someone argues that it's not true.  In this case, it took a week.
First, a little background.  Inflation in a cosmological sense refers to a period in the early Universe when the Universe as a whole expanded in a special way: specifically, the rate of expansion increased with time.  This was proposed to solve a number of problems with a simple Hot Big Bang model, including the non-observation of magnetic monopoles and the very small curvature of spacetime.  Inflation models need something to drive this expansion, and in Higgs inflation that something is the Standard Model Higgs field associated with the Higgs discovered nearly two years ago.  These models have two advantages: they are minimal, needing no new stuff beyond what we have already discovered; and they are testable.  Most inflationary models involve very heavy stuff we can never hope to produce on Earth, making them difficult to disprove.  In contrast, we already have a good handle on the properties of the Higgs and will only improve our understanding in the next decade or so.

To get inflation out of the Higgs, we have to couple it non-minimally to gravity.  This might sound counter to the first motivation above, but the relevant term is not forbidden so from the point of view of field theory must be included:
L = ξ H2 R
H is the Higgs, R the Ricci scalar (gravity), and ξ the coupling between the two.  We have to include this term to make the Higgs potential energy approximately constant over a large enough range of values of the Higgs field.  The normal argument against Higgs inflation is that we need a large value of ξ (~10000) to make inflation last long enough (to match CMB observations from WMAP and Planck).  Such values are then incompatible with large tensor fluctuations as observed by BICEP2.  This is the argument made in two recent papers, the first of which amusingly came out on the same day as the pro-Higgs inflation paper!

The way that Hamda et al get around this issue is by including quantum corrections to the Higgs potential.  It is now well-established that, with the measured values of the Higgs and top masses, the Higgs self-coupling approaches zero at high energies.  By tuning these values within the experimental uncertainties and including the effects of the non-minimal coupling, these authors claim to find a region where inflation lasts long enough with couplings ξ as small as 10.  An illustration of the tuning is shown in this plot:

Tiny differences in the top mass, of order 1 part in a million, substantially change the Higgs potential between regions that do and do not allow inflation.

There's a certain similarity here between this perspective and an increasingly common attitude in particle physics: that fine tuning is okay.  Indeed, you can argue that the SM Higgs is already fine-tuned to get the correct mass, more so if we demand nothing else all the way to the inflationary scale. So we have no further problem with tuning parameters to get inflation to work, as long as we remain within allowed parameter space.

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