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.