## Saturday, March 15, 2014

### B-modes, rumours, and inflation

Update: The announcement will definitely be about a major discovery by BICEP2, meaning it can only really be about a B-mode signal. You can follow the webcast at  http://www.cfa.harvard.edu/news/news_conferences.html, starting at 10:45 am EDT (14:45 GMT) for scientists, or 12:00 pm EDT (16:00 GMT) for the general public and news organisations.

The big news in cosmology circles at the minute is the rumour that the "major discovery" due to be announced at a press conference on Monday the 17th is in fact a claimed detection of the B-mode signal in the CMB by the the BICEP2 experiment.

Now, I'm not particularly well placed to comment on this rumour, since all the information I have comes at second- or third-hand, via people who have heard something from someone, people who think they heard something from someone, or people who are simply unashamedly speculating. (Perhaps this is a function of being on the wrong side of the Atlantic: although the BICEP2 experiment is based at the South Pole, the only non-North-American university participating in the collaboration is Cardiff University in Wales. Even worse, I'm not on Twitter.) In any case, by reading thisthisthis and this, you will be starting with essentially the same information as me.

But having got that health warning out of the way, let's pretend that the rumours are entirely accurate and that on Monday we will have an announcement of a detection of a significant B-mode signal. What would this mean for cosmology?

Firstly, the B-mode signal refers to a particular polarisation of the CMB (for a short and somewhat technical introduction, see here; for a slightly longer one, see here). This polarisation can arise in various ways, one of which is the polarisation induced in the CMB by gravitational lensing, as the CMB photons travel through the inhomogeneous Universe on their way from the last scattering surface to us. There have been a few experiments, such as POLARBEAR, which have already claimed a detection of this lensing contribution to the B-mode signal (though in this particular case after skim-reading the paper I was a little underwhelmed by the claim).

Now, detecting a lensing B-mode would be cool, but significantly less exciting than detecting a primordial B-mode. This is because whereas the lensing signal comes from late-time physics that is quite well understood, a primordial signal would be evidence of primordial tensor fluctuations or primordial gravitational waves. And this is cool because inflation provides a possible way to produce primordial gravitational waves – therefore their detection could be a major piece of evidence in favour of inflation.

 The contributions to the B-mode signal coming from gravitational waves and lensing are differentiated on the basis of the multipoles (essentially the length scale) at which they are important. Figure from Hu and Dodelson 2002.

People often say that detection of this tensor signal would be a "smoking gun" for inflation; something that would be very welcome, because although inflation has proved to be an attractive and fertile paradigm for cosmology, there is still a bit of a lack of direct, incontrovertible evidence in favour of it. Coupled with certain unresolved theoretical issues it faces, this lack of a smoking gun meant that arguments for or against inflation were threatening to degenerate into what you might call "multiverse territory", definitely an unhealthy place to be.

It may be worth introducing a note of caution about this "smoking gun" though. Although inflation is a possible source of primordial gravitational waves, it is not the only one. Artefacts of possible phase transitions in the early universe, known as cosmic defects, can also produce a spectrum of gravitational waves – and what's more, this spectrum can be exactly scale-invariant, just as that from inflation. I don't know a huge amount about this field, so I am not sure whether the amplitude of the perturbations which could be produced by these cosmic defects could be sufficiently large, nor – if it is – whether there are any other features which could help distinguish this scenario from inflation if the rumours turn out to be true. Perhaps better informed people could comment below.

Suppose we put that issue to one side though, and assume that not only has a significant tensor signal been detected, we have also been able to prove that it could not be due to anything other than inflation. The rumour is that the detection corresponds to value for the tensor-to-scalar ratio r of about 0.2. What are the implications of this for the different inflation models?

 Planck limits on various inflationary models.
Not all models of inflation do result in tensor modes large enough to observed in the CMB, so an observation of a large r would rule out a large class of these models. Generally speaking, the understanding is that models in which the inflaton field $\phi$ takes large values (i.e., values larger than the Planck mass $M_P$) are the ones which could produce observably large r, whereas the so-called "small-field models" where $\phi\ll M_P$ usually predict tiny values of r which could never be observed. (A note for non-experts: irrespective of the field value, the energy scale in both small-field and large-field models is always much less than the Planck scale.) Therefore, at a stroke, all small-field inflation models would be ruled out. Many people regard these as the better-motivated models of inflation, with in some respects fewer theoretical issues than the large-field models, so this would be quite significant.

There are two small caveats to this statement: firstly, it isn't strictly necessary for $\phi$ itself to be larger than $M_P$ to generate a large r, only that the change in $\phi$ be large. So models in which the inflaton field winds around a cylinder, in effect travelling a large distance without actually getting anywhere, can still give large r (hat-tip to Shaun for that phrasing). Also, it is not even strictly true that the change in $\phi$ must be large: if some other rather specific conditions (including the temporary breakdown of the slow-roll approximation) are met, this one can be avoided and even small field models can produce enough gravitational waves. This was something pointed out by a paper I wrote with Shaun Hotchkiss and Anupam Mazumdar in 2011, though other people had similar ideas at about the same time. Such rather forced small-field models would have other specific features though, so could be distinguished by other measurements.

One of the more interesting consequences of a detection of large r (aside from the earth-shattering importance of a confirmation of inflation itself) would be that the Higgs inflation model – which has been steadily gaining in popularity given the results from the LHC and Planck, and has begun to be regarded by many as the most plausible mechanism by which inflation could have occurred – would be disfavoured. In the plot above, the Higgs inflation prediction is shown by the orange points at the bottom centre of the figure. So a BICEP2 detection of $r\sim0.2$ as suggested by the rumours would be pretty serious for this model.

On the other hand, a BICEP2 detection of $r\sim0.2$ would also strongly contradict appear to be at odds with the results from the Planck and WMAP satellites. Which probably goes to show that there is not much point believing every rumour ...

We will find out on Monday!

1. Yes, that's true enough. Also, although I didn't mention it, the Planck constraints on $r$ shown in that figure are derived specifically assuming no running of the spectral index. Planck and WMAP could be perfectly consistent with a combination of a larger value of $r$ and a non-zero running. And yet another point is that Planck+WMAP constrain the value of $r$ at the pivot scale $k=0.002$ Mpc$^{-1}$, which will be larger than the scale at which BICEP measure it.
2. Basically, when I was writing this post in my mind the main point I was trying to make was about the consequences for inflation and different models of inflation of a measurably non-zero $r$. The comment at the end was a bit tongue-in-cheek and wasn't intended too seriously – though it appears that that's been the main point many readers have taken away from the post! I have therefore edited the sentence a little ...