Monday, March 24, 2014

BICEP2: reasons to be sceptical, part 2

This is the second part of three posts in which I wanted to lay out the various possible causes of concern regarding the BICEP2 result, and provide my own opinion on how seriously we should take these worries. I arranged these reasons to be sceptical into three categories, based on the questions
  • how certain can we be that BICEP2 observed a real B-mode signal?
  • how certain can we be that this B-mode signal is cosmological in origin, i.e. that it is due to gravitational waves rather than something less exciting?
  • how certain can we be that these gravitational waves were caused by inflation?
The first post dealt with the first of the three questions, this one addresses the second, and a post yet to be written will deal with the third.

How certain can we be that the observed B-mode signal is cosmological? 

Let's take it as given that none of the concerns in the previous post turn out to be important, i.e. that the observed B-mode signal is not an artefact of some hidden systematics in the analysis, leakage or whatever. From my position of knowing a little about data in general, but nothing much about CMB polarization analysis, I guessed that the chances of any such systematic being important were about 1 in 100.

The next question is then whether the signal could be caused by something other than the primordial gravitational waves that we are all so interested in. The most important possible contaminant here is other nearby sources of polarized radiation, particularly dust in our own Galaxy. We don't actually know how much polarized dust or synchrotron emission there might be in the sky maps here, so a lot of what BICEP have done is educated guesswork.

To start with, the region of the sky that BICEP looks at was chosen on the basis of a study by Finkbeiner et al. from 1999, which extrapolated from measurements of dust emission at certain other frequencies to estimate that, at the frequency of relevance to CMB missions such as BICEP, that particular part of the sky would be exceptionally "clean", i.e. with exceptionally low foreground dust emission. Whether this is actually true or not is not yet known for certain, but there exist a number of models of the dust distribution, and most of these models predict that the level of contamination to the B-mode detection from polarized dust emission would be an order of magnitude smaller than the observed signal. Similar model-dependent extrapolation to the observation frequency based on WMAP results suggests that synchrotron contamination is also an order of magnitude too small.

Predictions for foreground contamination for different dust models (the coloured lines at the bottom) versus the actual B-mode signal observed by BICEP2 (black points).

Now one real test of these assumptions will come from Planck, because Planck will soon have the best map of dust in our Galaxy and therefore the best limits on the possible contamination. This is one of the reasons to look forward to Planck's own polarization results, due in about October or November. In the absence of this information, the other thing that we would like to see from BICEP in order to be sure their signal is cosmological is evidence that the signal exists at multiple frequencies (and has the expected frequency dependence).

BICEP do not detect the signal at multiple frequencies. The current experiment, BICEP2, operates at 150 GHz only, and that is where the signal is seen. A previous experiment, BICEP1, did run at 100 GHz as well, but BICEP1 did not have the same sensitivity and could only place an upper limit on the B-mode signal. Data from the Keck Array will eventually also include observations at 100 GHz, but this is not yet available. Until we have confirmation of the signal at different frequencies, most cosmologists will treat the result very carefully.

In the absence of this, we must look at the cross-correlation between B2 and B1. Remember that although B1$\times$B1 did not have the sensitivity to make a detection of non-zero power, B2$\times$B1 can still tell us something useful. If B1 maps were purely noise, or B2 maps were due to dust, we would not expect them to be correlated. If both were due to synchrotron radiation, we would expect them to be strongly correlated. In fact the B2$\times$B1 cross power is non-zero at the $3\sigma$ level or about 99% confidence, which is something Peter Coles' sceptical summary ignores. This is indeed evidence that the signal seen at 150 GHz is cosmological.

Still, some level of cross-correlation could be produced even if both B2 and B1 were only seeing foregrounds. Combining the B2$\times$B1 data with B2$\times$B2 and B1$\times$B1 means that polarized dust or synchrotron emission of unexpected strength are rejected as explanations – though at a not-particularly-exciting significance of about $2.2-2.3\sigma$.


It's fair to say, on the basis of models of the distribution of polarized dust and synchrotron emission, that the BICEP2 signal probably isn't due to either of these contaminants. However, we don't yet have confirmation of the detection at multiple frequencies, which is required to judge for sure. At the moment, the frequency-based evidence against foreground contamination is not very strong, but we'd still need some quite unexpected stuff to be going on with the foregrounds to explain the amplitude of the observed signal.

Overall, I'd guess the odds are about 1:100 against foregrounds being the whole story. (This should still be compared with the quoted headline result of 1:300,000,000,000 against $r=0$ assuming no foregrounds at all!)

The chances are much higher – I'd be tempted to say perhaps even as much as better than even money – that foregrounds contribute a part of the observed signal, and that therefore the actual value of the tensor-to-scalar ratio will come down from $r=0.2$, perhaps to as low as $r=0.1$, when Planck checks this result using their better dust mapping.

Friday, March 21, 2014

BICEP2: reasons to be sceptical, part 1

As the dust begins to settle following the amazing announcement of the discovery of gravitational waves by the BICEP2 experiment, physicists around the world are taking stock and scrutinizing the results.

Remember that the claimed detection is enormously significant, in more ways than one. The BICEP team have apparently detected an exceedingly faint B-mode polarization pattern in the CMB, at an order of magnitude better sensitivity than any previous experiment probing the same scales. They have then claimed to have been able to ascribe this B-mode signal unambiguously to cosmological gravitational waves, rather than any astrophysical effects due to intervening dust or other sources of radiation. And finally they have interpreted these results as direct evidence for the theory of inflation, which is really the source of all the excitement, because if true it would pin down the energy scale of inflation at an incredibly high level, with extensive and dramatic consequences for our understanding of high energy particle physics.

However, as all physicists have been saying, with results of this magnitude it is important to be very careful indeed. Speculating who should get the Nobel Prize (or Prizes) for this is still premature. The paper containing the results will of course be subjected to anonymous peer review when it is submitted to a journal, but it has also already faced a rather extraordinary open peer review by social media, with a live group on Facebook, and all sorts of other discussion on blogs, Twitter and the like. (And to the great credit of the scientists on the BICEP team, they have patiently responded to questions and comments on these forums, and the whole process has been carried out very civilly!)

What I wanted to do today is to possibly contribute to that by gathering together all the main points of concern and reasons to be sceptical of the BICEP result. This is partly for my own purposes, since writing things down helps to clarify my thoughts. I will divide these concerns into three main categories, addressing the following questions:

  • how certain can we be that BICEP2 observed a real B-mode signal?
  • how certain can we be that this B-mode signal is cosmological in origin, i.e. that it is due to gravitational waves rather than something less exciting?
  • how certain can we be that these gravitational waves were caused by inflation?

I'll discuss the first category of concerns in part 1 of this post and the next two together in parts 2 and 3. I do not claim that any of the concerns I raise here are original, however any mistakes are definitely mine alone. I'd like to encourage discussion of any of these points via the comments below.

How certain can we be that BICEP2 observed a real B-mode signal?

This is obviously the most basic issue. The general reason for concern here — and this applies to any B-mode detection experiment — is that the experimental pipeline has to be able to decompose the polarization signal seen into two components, the E-mode and the B-mode, and the level of the signal in the B-mode is orders of magnitude smaller than in E. Now, as Peter Coles explains here, the E and B polarization components are in principle orthogonal to each other when the spherical harmonic decomposition can be performed over the whole sky, but this is in practice impossible. BICEP observes only a small portion of the sky, and therefore there is the possibility of "leakage" from E to B when the separating out the components. It would not take much leakage to spoil the B-mode observation.

Obviously the BICEP team implemented many tests of the obtained maps to check for such systematics. One of the ways to do this is to cross-correlate the E and B maps: if there is no leakage the cross-correlation should be consistent with zero. Another important test is the jackknife technique, also nicely explained here: you split your data into two equal halves, and subtract the signal found in one half from that in the other; the answer should also be consistent with zero.

Now one source of concern arises because of a combination of these two tests. The blue points in the following figure show the results of a jackknife test on the BB power:

These points are consistent with zero ... but they are possibly too consistent with zero! The $1\sigma$ error bars of each one of them passes through zero, whereas it would be more natural to expect some more scatter. In fact from the number on the plot you can see that there is only a 1% chance that all 9 blue points should be so close to zero.

This raises the possibility, pointed out by Hans Kristian Eriksen, that the errorbars on the blue points are overestimated. It may then be the case that the errorbars on other points in other jackknife tests are also too large. If that were the case then reducing those errors might mean that some of the other jackknife tests now fail — the points are no longer consistent with zero. As it happens, of the 168 jackknife test results listed in the table in the paper, quite a large number (about 7) of them already "fail" by the stricter standards (2% probability) some other experiments such as QUIET might apply. Obviously some number of tests are always expected to fail, but more than 7 out of 168 starts to look like quite a large number. This then becomes a little worrying.

On the other hand, this extrapolation may be a little exaggerated, because we are surmising that the errorbars might be too large purely on the basis of the one figure above. Clearly if you do a large number of jackknife tests, it becomes less surprising that one of them gives a surprising result, if you see what I mean. Looking through the table for the other BB jackknife results, the particular example from the figure is the only one that stands out as being odd, so it is hard to conclude from this that the errorbars are too large. Overall I'm not convinced that there is necessarily a problem here, but it is something that deserves a little more quantitative attention.

The second source of concern that has been highlighted is that the data at large multipole values appear to be doing something odd. Look at the 5th, 6th and 7th black points from the figure above, which are quite a long way from the theoretical expectation. Peter Coles helpfully drew a little blue circle around them:

The worry here is that even if the data appear to be passing jackknife tests for internal consistency and null tests for EB cross power, the fact that these points are so high suggests that there is still some undetected systematic that has crept in somewhere. This hypothesized systematic could account for the measured values of the crucial first four points, which constitute the detection of the gravitational waves.

Similarly, people are worried about the EE power spectrum, which appears to be too high in the $50< \ell<100$ region — again this could be a sign of leakage from temperature into polarization, which could perhaps be contaminating the B-mode maps despite not explicitly showing up in the jackknife consistency checks.

Now, the BICEP response to this is that you shouldn't judge things simply "by eye". The EE excess does not appear to be statistically significant. It's also not incredibly unlikely that the final two of the circled BB data points could simultaneously be as high as they are just due to random chance — they say "their joint significance is $<3\sigma$", which means that the chance is about 1%. (Of course the chance that all three of the circled points could simultaneously be high is smaller than that, and so presumably less than 1% ... )

Another justification some people have been providing (mostly people from outside the BICEP collaboration to be fair, though some from within it as well) is that the preliminary data from the Keck array, which is a similar instrument to BICEP but with higher sensitivity, appear to show no anomaly in that region. I think this is a somewhat dangerous argument, because the Keck data also don't seem to be quite so high in the region of the crucial first four bandpowers! In any case, the "official" word from BICEP is that any such speculation on the basis of Keck is to be discouraged, because the Keck data is still very preliminary and has not been properly checked.


I'm a little bit worried about the various issues raised here, though overall I would say the odds are in favour of the B-mode detection being secure (this is a different issue to whether this detected signal is due to gravitational waves! More on that in the next post). I would not, however, put those odds at anywhere near 1 in 300,000,000,000 against there being an error, which is the headline significance claimed for the detection of a non-zero tensor-to-scalar ratio ($7\sigma$). If I were forced to quantify my belief, I would say something more like 1 or 2 in 100. That's not particularly secure, but luckily there are follow-up experiments, such as Keck and Planck itself, which should be able to reassure us on that score soon.

A final point: seeing the preliminary Keck data shown in a figure in the paper suggests to me that perhaps the final analysis of Keck data will now not be done "blind". I hope that's not the case, it would be very disturbing indeed if it were. 

Monday, March 17, 2014

First Direct Evidence for Cosmic Inflation

That was the title of the BICEP2 presentation today. Gives you some idea about the magnitude of the result, if it holds up: it really is astonishingly exciting.

Unfortunately it was so exciting that we in Helsinki couldn't even access the Harvard server and so couldn't watch any of the webcast at all. It seems the same was true for most other cosmologists around the world. So my comments here are based purely on a preliminary reading of the paper itself, and a distillation of the conversations occurring via Facebook and the like.

Firstly, the headline results: the BICEP team claim to have detected a B-mode signal in the CMB at exceedingly high statistical significance. Their headline claim is

$r=0.2^{+0.07}_{-0.05}$, with $r=0$ disfavoured at $7.0\sigma$

That is frankly astonishing. Here's the likelihood plot:

BICEP2 constraint on the tensor-to-scalar ratio r. 

(All figures are taken from the paper avalaible here.)

The actual measurement of the BB power spectrum looks like this:

The black points are the new measurements, the other coloured points are the previously available best upper limits. The solid red curve is the theoretical expectation from lensing (the relatively boring contribution to BB), the dashed red curve that dies off is the theoretical expectation from a model with inflationary gravitational waves and $r=0.2$, and the other dashed red curve (were they short of colours?!) is the total.

They've also done a pretty good job of eliminating other foreground sources (dust, synchrotron emission etc.) as possible explanations for the signal seen, which means it is much more likely that the signal is actually due to primordial gravitational waves from inflation. In doing this, it helps that the signal they see is actually as large as it is, since there's less chance of confusing it with these foregrounds (which are much smaller).  [Update: I'm not an expert here, apparently some others were less convinced about the removal of foregrounds. Not sure why though – I'd have thought other systematic errors were far more likely to be a problem than foregrounds.]

So far so good. In fact — and I really can't stress this enough — this is an extraordinary, wonderful, unexpected result and huge congratulations to the BICEP team for achieving it. It will mean a lot of happy theorists as well, because we finally have something new to try to explain!

However, it is very important that as a community we remain skeptical, particularly so when - as here - the result is one that we would so desperately love to be true. Given that, I'm going to list a serious of things that are potentially worrying/things to think about/things I don't understand. (Some of these are not things I noticed myself, but were points raised by Dave Spergel, Scott Dodelson and other experts at the ongoing live discussion on Facebook.) Doubtless these are questions the BICEP team will have thought about themselves; perhaps they already have all the answers and will tell us about them in due course — as I said, no one I know was able to watch the webcast live.

  • In the BB-spectrum plot above, the data seem to be showing a significant excess above expectations for multipoles about $\ell\sim200-350$. What's going on with that?
  • This is particularly noticeable in another figure (Fig. 9) in the paper:
  • From the above figure, preliminary results of the cross-correlation with Keck don't show the excess at high-$\ell$ (a reason to believe it might go away), but the same cros-correlation also shows less power at lower $\ell$ (which is a bit confusing).
  • At lower values of $\ell$ the EE power spectrum also shows an excess (Fig. 7):
  • All the above points put together suggest that perhaps there is some leakage in the polarisation maps coming from the temperature anisotropy — a large part of the analysis work is concerned with accounting for and correcting for any such leakage, of course, the question is to what extent independent experts will be satisfied that these methods worked.
  • Although the headline figure is $r=0.2$, they rather confusingly later say that when the best possible dust model is used for foreground subtraction, this becomes $r=0.16^{+0.06}_{-0.05}$. But if this the the best possible dust model, why is this not the quoted headline number? Is this related somehow to the power excess at $\ell\sim200-350$?
  • If $r$ is as large as they have measured why was it not seen by Planck? Actually this is a fairly complicated question: the point being that if the tensor amplitude is so large, it should make a non-negligible contribution to the temperature power spectrum as well, which would have affected Planck's results. Planck had a constraint $r<0.11$, but this specifically assumed that the primordial power spectrum had a power-law form with no running (sorry about the technical jargon, unfortunately not enough time to explain here today). So BICEP suggest one way around this tension is to simply introduce a running, but it seems (but this bit was not entirely clear to me from the paper) that you need a fairly large value of the running for this explanation to fly. And if you've got a large running then you have to worry about why not a running of the running, a running of the running of the running and so on ad infinitum - in fact how do we know that the power-law expansion form of the $P(k)$ is the correct way to go at all?
  • Besides, are there viable inflationary models that predict both large $r$ as well as large running (or non-power-law form of the primordial power)? Given the vast array of inflationary models, the answer to this question is almost certainly yes, but people may consider some other explanations more worthwhile ...
Phew. There are probably lots of other things to think about, but that's about all I can manage today. It's been a very exciting day!

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, 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!

Monday, February 3, 2014

Does the multiverse explain the cosmological constant?

At the end of the last post on falsifiability, I mentioned the possibility that the multiverse hypothesis might provide an explanation for the famous cosmological constant problem. Today I'm going to try to elaborate a little on that argument and why I find it unconvincing.

Limitations of space and time mean that I cannot possibly start this post as I would like to, with an explanation of what the cosmological problem is, and why it is so hard to resolve it. Readers who would like to learn a bit more about this could try reading this, this, this or this (arranged in roughly descending order of accessibility to the non-expert). For my purposes I will have to simply summarise the problem by saying that our models of the history of the Universe contain a parameter $\rho_\Lambda$ – which is related to the vacuum energy density and sometimes called the dark energy density – whose expected value, according to our current understanding of quantum field theory, should be at least $10^{-64}$ (in units of the Planck scale energy) and quite possibly as large as 1, but whose actual value, deduced from our reconstruction of the history of the Universe, is approximately $1.5\times10^{-123}$. (As ever with this blog, the mathematics may not display correctly in RSS readers, so you might have to click through.)

This enormous discrepancy between theory and observation, of somewhere between 60 and 120 orders of magnitude, has for a long time been one of the outstanding problems – not to say embarrassments – of high energy theory. Many very smart people have tried many ingenious ways of solving it, but it turns out to be a very hard problem indeed. Sections 2 and 3 of this review by Raphael Bousso provide some sense of the various attempts that have been made at explanation and how they have failed (though this review is unfortunately also at a fairly technical level).

This is where the multiverse and the anthropic argument comes in. In this very famous paper back in 1987, Steven Weinberg used the hypothesis of a multiverse consisting of causally separated universes which have different values of $\rho_\Lambda$ to explain why we might be living in a universe with a very small $\rho_\Lambda$, and to predict that if this were true, $\rho_\Lambda$ in our universe would nevertheless be large enough to measure, with a value a few times larger than the energy density of matter, $\rho_m$. This was particularly important because the value of $\rho_\Lambda$ had not at that time been conclusively measured, and many theorists were working under the assumption that the cosmological constant problem would be solved by some theoretical advance which would demonstrate why it had to be exactly zero, rather than some exceedingly small but non-zero number.

Weinberg's prediction is generally regarded as having been successful. In 1998, observations of distant supernovae indicated that $\rho_\Lambda$ was in fact non-zero, and in the subsequent decade-and-a-half increasingly precise cosmological measurements, especially of the CMB, have confirmed its value to be a little more than three times that of $\rho_m$.

This has been viewed as strong evidence in favour of the multiverse hypothesis in general and in particular for string theory, which provides a potential mechanism for the realisation of this multiverse. Indeed in the absence of any other observational evidence for the multiverse (perhaps even in principle), and the ongoing lack of experimental lack of experimental evidence for other predictions of string theory, Weinberg's anthropic prediction of the value of the cosmological constant is often regarded as the most important reason for believing that these theories are part of the correct description of the world. For instance, to provide just three arbitrarily chosen examples, Sean Carroll argues this here, Max Tegmark here, and Raphael Bousso in the review linked to above.

I have a problem with this argument, and it is not a purely philosophical one. (The philosophical objection is loosely the one made here.) Instead I disagree that Weinberg's argument still correctly predicts the value of $\rho_\Lambda$. This is partly because Weinberg's argument, though brilliant, relied upon a few assumptions about the theory in which the multiverse was to be realised, and theory has subsequently developed not to support these assumptions but to negate them. And it is partly because, even given these assumptions, the argument gives the wrong value when applied to cosmological observations from 2014 rather than 1987. Both theory and observation have moved away from the anthropic multiverse.

Wednesday, January 22, 2014

Is falsifiability a scientific idea due for retirement?

Sean Carroll argues that it is.

He characterises the belief that "theories should be falsifiable" as a "fortune-cookie-sized motto"; it's a position adopted only by "armchair theorizers" and "amateur philosophers", and people who have no idea how science really works. He thinks we need to move beyond the idea that scientific theories need to be falsifiable; this appears to be because he wants to argue that string theory and the idea of the multiverse are not falsifiable ideas, but are still scientific.

This position is not just wrong, it's ludicrous. 

What's more, I think deep down Sean – who is normally a clear, precise thinker – realises that it is ludicrous. Midway through his essay, therefore, he flaps around trying to square the circle and get out of the corner he has painted himself into: a scientific theory must, apparently, still be "judged on its ability to account for the data", and it's still true that "nature is the ultimate guide". But somehow it isn't necessary for a theory to be falsifiable to be scientific.

Now, I'm not a philosopher by training. Therefore what follows could certainly be dismissed as "amateur philosophising". I'm almost certain that what I say has been said before, and said better, by other people in other places. Nevertheless, as a practising scientist with an argumentative tendency, I'm going to have to rise to the challenge of defending the idea of falsifiability as the essence of science. Let's start by dismantling the alternatives.

Wednesday, January 15, 2014

A new start to blogging in 2014

Well, Blank On The Map has been sadly silent for rather longer than I intended.

There were several reasons for this. I mentioned one of them in the last post on here a few months ago – the need to put my nose to the postdoc research grindstone in order to try to avoid being scooped. As it turns out, we were scooped after all, but there is still more to be said on the matter and in any case the result we were gunning for turned out to be not quite so exciting as we were hoping. More news on that in some future posts perhaps.

Another reason for radio silence was that I found that quite a lot of my work over the last couple of months has turned out to involve more intensive writing – including a lot of time worrying over the careful choice of words, precise phrasing and tone of my written output – than I'd have liked, and almost more of that than actual research. This was mostly because of a recent paper I wrote which led to a bit of a bad-tempered spat ... anyway, the upshot of this was that I did not feel much in the mood for more writing on here.

It also turns out that any kind of a break from blogging is sort of self-sustaining. When you haven't have much time for writing, the simple fact of its scarcity makes you start to place unreasonably high expectations on your output: is this topic really more interesting than that other topic I didn't have time to write about last week?

Ah well. I'll start the new year with this simple post, which also serves as a way of mentioning that I've moved universities and countries: I now live in Helsinki, and work at the University of Helsinki and the Helsinki Institute of Physics. As a result, I now have a new webpage! (Indeed, for complicated reasons, I actually have a second one as well, but it's got the same content.)

When I arrived here in October, Helsinki looked like this:

Now it looks like this:

The next post of this year will deal with more interesting topics!

Monday, September 2, 2013

A long summer

Indeed it has been a long summer, though the good weather appears to be drawing to a close. Over the last few months, I have attended three cosmology conferences or workshops and also been on a two-week holiday in the Dolomites, where I occupied my time by doing things like this:

La Guglia Edmondo de Amicis, near the Misurina lake.
and enjoying views like this:

Cima Piccola di Lavaredo, from the Dibona route on Cima Grande.
This explains the lack of activity here in recent times.

Returning home a couple of weeks ago, I was full of ideas for several exciting blog posts, including a summary of all the hottest topics in cosmology that were discussed at the conferences I attended, and perhaps an account of my argument stimulating discussion with Uros Seljak. However, it has come to my attention that there are other physicists in other parts of the world who happen to be working on the exact same topic that my collaborators and I have been investigating for the last few months. The rule in the research world is of course "publish or perish" (though some wit has suggested that "publish and perish" is more accurate) – so most of my time now will be spent on avoiding being scooped, and the current hiatus on this blog will continue for a short period. Looking on the bright side, once normal service resumes, I hope to have some interesting science results to describe!

In the meantime, I can only direct you to other blogs for your entertainment and enlightenment. Those of you who like physics discussions and have not already read Sean Carroll's blog (a vanishingly small number perhaps?) might enjoy this post about Boltzmann brains. I personally also enjoyed this argument against philosopher Tom Nagel.

For people interested in climbing news, I can report that my friends on the Oxford Greenland Expedition that I mentioned once here have returned safely after a successful series of very impressive climbs. I found their regular reports of their activities in the expedition diary well-written and rather thrilling – not just the climbing, but also the account of the journey to Greenland by sea in the face of seemingly never-ending gales! Well worth a read, as is this.

Thursday, July 11, 2013

Quasars, homogeneity and Einstein

[A little note: This post, like many others on this blog, contains a few mathematical symbols which are displayed using MathJax. If you are reading this using an RSS reader such as Feedly and you see a lot of $ signs floating around, you may need to click through to the blog to see the proper symbols.]

People following the reporting of physics in the popular press might remember having come across a paper earlier this year that claimed to have detected the "largest structure in the Universe" in the distribution of quasars, that "challenged the Cosmological Principle". This was work done by Roger Clowes of the University of Central Lancashire and collaborators, and their paper was published in the Monthly Notices of the Royal Astronomical Society back in March (though it was available online from late last year). 

The reason I suspect people might have come across it is that it was accompanied by a pretty extraordinary amount of publicity, starting from this press release on the Royal Astronomical Society website. This was then taken up by Reuters, and featured on various popular science websites and news outlets, including New ScientistThe Atlantic, National Geographic,, The Daily Galaxy, Phys.orgGizmodo, and many more. The structure they claimed to have found even has its own Wikipedia entry.

Obligatory artist's impression of a quasar.

One thing that you notice in a lot of these reports is the statement that the discovery of this structure violates Einstein's theory of gravity, which is nonsense. This is sloppy reporting, sure, but the RAS press release is also partly to blame here, since it includes a somewhat gratuitous mention of Einstein, and this is exactly the kind of thing that non-expert journalists are likely to pick up on. Mentioning Einstein probably helps generate more traffic after all, which is why I've put him in the title as well.

But aside from the name-dropping, what about the main point about the violation of the cosmological principle? As a quick reminder, the cosmological principle is sometimes taken to be the assumption that, on large scales, the Universe is well-described as homogeneous and isotropic. 

The question of what constitutes "large scales" is sometimes not very well-defined: we know that on the scale of the Solar System the matter distribution is very definitely not homogeneous, and we believe that on the scale of size of the observable Universe it is. Generally speaking, people assume that on scales larger than about $100$ Megaparsecs, homogeneity is a fair assumption. A paper by Yadav, Bagla and Khandai from 2010 showed that if the standard $\Lambda$CDM cosmological model is correct, the scale of homogeneity must be less than at most $370$ Mpc. 

On the other hand, this quasar structure that Clowes et al. found is absolutely enormous: over 4 billion light years, or more than 1000 Mpc, long. Does the existence of such a large structure mean that the Universe is not homogeneous, the cosmological principle is not true, and the foundation on which all of modern cosmology is based is shaky?

Well actually, no. 

Unfortunately Clowes' paper is wrong, on several counts. In fact, I have recently published a paper myself (journal version here, free arXiv version here) which points out that it is wrong. And, on the principle that if I don't talk about my own work, no one else will, I'm going to try explaining some of the ideas involved here.

The first reason it is wrong is something that a lot of people who should know better don't seem to realise: there is no reason that structures should not exist which are larger than the homogeneity scale of $\Lambda$CDM. You may think that this doesn't make sense, because homogeneity precludes the existence of structures, so no structure can be larger than the homogeneity scale. Nevertheless, it does and they can.

Let me explain a little more. The point here is that the Universe is not homogeneous, at any scale. What is homogeneous and isotropic is simply the background model we use the describe its behaviour. In the real Universe, there are always fluctuations away from homogeneity at all scales – in fact the theory of inflation basically guarantees this, since the power spectrum of potential fluctuations is close to scale-invariant. The assumption that all cosmological theory really rests on is that these fluctuations can be treated as perturbations about a homogeneous background – so that a perturbation theory approach to cosmology is valid.

Given this knowledge that the Universe is never exactly homogeneous, the question of what the "homogeneity scale" actually means, and how to define it, takes on a different light. (Before you ask, yes it is still a useful concept!) One possible way to define it is as that scale above which density fluctuations $\delta$ generally become small compared to the homogeneous background density. In technical terms, this means the scale at which the two-point correlation function for the fluctuations, $\xi(r)$, (of which the power spectrum $P(k)$ is the Fourier transform) becomes less than $1$. Based on this definition, the homogeneity scale would be around $10$ Mpc.

It turns out that this definition, and the direct measurement of $\xi(r)$ itself, is not very good for determining whether or not the Universe is a fractal, which is a question that several researchers decided was an important one to answer a few years ago. This question can instead be answered by a different analysis, which I explained once before here: essentially, given a catalogue with the positions of many galaxies (or quasars, or whatever), draw a sphere of radius $R$ around each galaxy, and count how many other galaxies lie within this sphere, and how this number changes with $R$. The scale above which the average of this number for all galaxies starts scaling as the cube of the radius, $$N(<R)\propto R^3,$$ (within measurement error) is then the homogeneity scale (if it starts scaling as some other constant power of $R$, the Universe has a fractal nature). This is the definition of the homogeneity scale used by Yadav et al. and it is related to an integral of $\xi(r)$; typically measurements of the homogeneity scale using this definition come up with values of around $100-150$ Mpc.

The figure that proves that the distribution of quasars is in fact homogeneous on the expected scales. For details, see  arXiv:1306.1700

To get back to the original point, neither of these definitions of the homogeneity scale makes any claim about the existence of structures that are larger than that. In fact, in the $\Lambda$CDM model, the correlation function for matter density fluctuations is expected to be small but positive out to scales larger than either of the two homogeneity scales defined above (though not as large as Yadav et al.'s generous upper limit). The correlation function that can actually be measured using any given population of galaxies or quasars will extend out even further. So we already expect correlations to exist beyond the homogeneity scale – this means that, for some definitions of what constitutes a "structure", we expect to see large "structures" on these scales too.

The second reason that the claim by Clowes et al. is wrong is however less subtle. Given the particular definition of a "structure" they use, one would expect to find very large structures even if density correlations were exactly zero on all scales.

Yes, you read that right. It's worth going over how they define a "structure", just to make this absolutely clear. About the position of each quasar in the catalogue they draw a sphere of radius $L$. If any other quasars at all happen to lie within this sphere, they are classified as part of the same "structure", which can now be extended in other directions by repeating the procedure about each of the newly added member quasars. After repeating this procedure over all $18,722$ quasars in the catalogue, the largest such group of quasars identified becomes the "largest structure in the Universe".

It should be pretty obvious now that the radius $L$ chosen for these spheres, while chosen rather arbitrarily, is crucial to the end result. If it is too large, all quasars in the catalogue end up classified as part of the same truly ginormous "structure", but this is not very helpful. This is known as "percolation" and the critical percolation threshold has been thoroughly studied for Poisson point sets – which are by definition random distributions of points with no correlation at all. The value of $L$ that  Clowes et al. chose to use, for no apparent reason other than that it gave them a dramatic result, was $100$ Mpc – far too large to be justified on any theoretical grounds, but slightly lower than the critical percolation threshold would be if the quasar distribution was similar to that of a Poisson set. On the other hand, the "largest structure in the Universe" only consists of $73$ quasars out of $18,722$, so it could be entirely explained as a result of the poor definition ...

Now I'll spare you all the details of how to test whether, using this definition of a "structure", one would expect to find "structures" extending over more than $1000$ Mpc in length or with more than $73$ members or whatever, even in a purely random distribution of points, which are by definition homogeneous. Suffice it to say that it turns out one would. This plot shows the maximum extent of such "structures" found in $10,000$ simulations of completely uncorrelated distributions of points, compared to the maximum extent of the "structure" found in the real quasar catalogue.

The probability distribution of extents of largest "structures" found in 10,000 random point sets for two different choices of $L$. Vertical lines show the actual values found for "structures" in the quasar catalogue. The actual values are not very unusual. Figure from arXiv:1306.1700

To summarise then: finding a "structure" larger than the homogeneity scale does not violate the cosmological principle, because of correlations; on top of that, the "largest structure in the Universe" is actually not really a "structure" in any meaningful sense. In my professional opinion, Clowes' paper and all the hype surrounding it in the press is nothing more than that – hype. Unfortunately, this is another verification of my maxim that if a paper to do with cosmology is accompanied by a big press release, it is odds-on to turn out to be wrong.

Finally, before I leave the topic, I'll make a comment about the presentation of results by Clowes et al. Here, for instance, is an image they presented showing their "structure", which they call the 'Huge-LQG', with a second "structure" called the 'CCLQG' towards the bottom left:

3D representation of the Huge-LQG and CCLQG. From arXiv:1211.6256.

Looks impressive! Until you start digging a bit deeper, anyway. Firstly, they've only shown the quasars that form part of the "structure", not all the others around it. Secondly, they've drawn enormous spheres (of radius $33$ Mpc) at the position of each quasar to make it look more dramatic. In actual fact the quasars are way smaller than that. The combined effect of these two presentational choices is to make the 'Huge-LQG' look far more plausible as a structure than it really is. Here's a representation of the exact same region of space that I made myself, which rectifies both problems:

Quasar positions around the "structures" claimed by Clowes et al.

Do you still see the "structures"?

Sunday, June 23, 2013

Across the Himalayan Axis

I had promised to try to write a summary of the workshop on cosmological perturbations post Planck that took place in Helsinki in the first week of June, but although the talks were all interesting, I didn't feel very inspired to write much about them. Plus life has been intervening, so I'll have to leave you to read Shaun's accounts at the Trenches of Discovery instead.

I also recently put a new paper on the arXiv; despite promising to write about my own papers when I put them out, I'm going to have to postpone an account of this one until next week. This is because I am spending the next week at a rather unique workshop in the Austrian Alps. (This is one of the perks of being a physicist, I suppose!)

Therefore today's post is going to be about mountaineering instead. It is an account I wrote of a trek I did with my father and sister almost exactly seven years ago: we crossed the main Himalayan mountain range from south to north over a mountain pass known as the Kang La (meaning 'pass of ice' in the local Tibetan dialect, I believe), and then crossed back again from north to south over another pass as part of a big loop. In doing so we also crossed from the northern Indian state of Himachal Pradesh into Zanskar, a province of the state of Jammu and Kashmir, and then back again.

The account below was first written as a report for the A.C. Irvine Travel Fund, who partly funded this trip, and it has been available via a link on their website for several years. At the time, the Kang La was a very infrequently-used pass, in quite a remote area and only suitable for strong hikers with high-altitude mountain experience. But in the seven years since my trip it has seen quite a rise in popularity — I sometimes flatter myself that my account had something to do with raising the profile of the area!

Anyway, the account itself follows after the break. There is also a sketch map of the area I drew myself (it's hard to obtain decent cartographical maps of the area, and illegal to possess them in India due to the proximity to the border), and a few photographs to illustrate the scenery ...