At a time when many cosmic inflation theory fans are jumping the gun and popping champagne corks over Monday's BICEP2 study results, calling it an epic breakthrough, I hate to be a killjoy. I like to join a party as much as the next man. The problem is that I keep finding reasons for doubting the claims made about the study, that it provides evidence for the theory of cosmic inflation. My main reasons were given in this blog post, and some lesser software-related reasons were given in yesterday's blog post. Now I will discuss a very big additional reason for doubting the claims being made about BICEP2, a reason I haven't previously discussed: their main graph has a very dubious feature, a curve that is quite misleading.
The BICEP2 paper has two versions of the graph, one that is logarithmic and another that is not. Below is the non-logarithmic version, which makes it easier to see how the discovered data does not match what is predicted from the theory of cosmic inflation:
In this graph the black dots represent the new BICEP2 observations of b-mode polarization. The vertical lines are error bars representing uncertainty in the data. The bottom dashed line is a prediction of b-mode polarization made by one version of the theory of cosmic inflation (a “wishful thinking” version chosen by the BICEP2 team, as I will explain in a minute). The solid line represents contributions to b-mode polarization projected to occur from gravitational lensing. The upper dashed curved line represents the b-mode polarization that could occur from a combination of gravitational lensing and the version of the inflation theory that was chosen by the BICEP2 team to make their data match inflation theory.
Now the untrained eye can spot a big problem with this graph: the observations do not match what is expected. While the first two black dots match the top dashed line (as does the last black dot), several of the other black dots are way above the top dashed line, in particular and seventh and eighth dots. On this basis, we are entitled to say: inflation theory falls way short.
But here is a very important fact about this graph: the bottom curved hill-shaped dashed line (the supposed contributions from cosmic inflation) is not “the” prediction from the theory of cosmic inflation. It is instead the prediction from a particular version of the inflation theory carefully chosen by the BICEP2 team so that their observational results can be matched to inflation theory. The version in question is one that drastically contradicts conclusions made with a 95% confidence level last year by a much larger team of scientists, using the Planck space observatory.
The “prediction from inflation” that appears as the hill-shaped red dashed line on the above graph all depends on a particular data item called the tensor-to-scalar ratio, which cosmologists represent with the letter r. In a scientific paper co-authored last year by more than 200 scientists, the Planck team concluded with a 95% confidence level that this tensor-scalar ratio is less than .11. But in the graph above the BICEP2 team chose to disregard these findings, and use on their graph an extreme version of the inflation theory in which the tensor-scalar ratio is .2 (200% higher than the maximum value set by the larger group of scientists).
Why would the BICEP2 team have done that? Because it allowed them to produce a graph showing a partial match between their observations and the predictions of a cosmic inflation theory. A triumph of wishful thinking. It's rather like a husband reassuring his wife by showing her a graph in which his projected income rises by 50% for each of the next five years.
But what would the key BICEP2 graph have looked like if they had accepted the limit set by the much larger Planck team? The graph would have looked rather like the graph below, except that the left half of the top red dashed line would have to be dropped way down, and none of the observations would be anywhere near close to matching the predictions from inflation (except for the last one, at a point in the graph where inflation is irrelevant, and all contribution is from gravitational lensing).
The BICEP2 team could have produced a graph like the one above (but with the left half of the top dashed line dropped way down, to equal the green line plus the solid red line). That is exactly what they should have done. They might then have made an announcement like this:
We have some interesting new observations. But we're sorry to report that, respecting the limits set last year by a much larger team of scientists, our observations provide no evidence to back up the theory of cosmic inflation.
Instead, the BICEP2 team chose to put in a bogus red dashed line in their key graph, representing a farfetched, extreme wishful-thinking version of the cosmic inflation theory, one that relies on a version of inflation with a tensor-scalar ratio (r) about twice as high as the maximum allowed value according to the larger Planck team. Rather than candidly showing such a red-dashed line as just one possible version of inflation, they put it on the graph as if it was the only version of inflation.
It was a great way to grab press headlines, but not very honest or candid.
When we use the predictions of inflation using the Planck team's estimate of the upper limit of the tensor-scalar ratio (with a 95% confidence level), corresponding roughly to the green line in the graph above, we are led to think that the BICEP2 team's observations provide no support to a theory of cosmic inflation.
Postscript: This post uses the assumption that smaller values for the tensor-to-scalar ratio (r) cause the "hill" of the inflation prediction to drop much smaller, a point that is clear from looking at this site.