# Which BICEP2 r value should be compared to Planck's r<0.11?

The BICEP2 paper reports a tensor/scalar ratio $r = 0.20_{-0.05}^{+0.07}$, but then says:

Subtracting the various dust models and re-deriving the r constraint still results in high significance of detection. For the model which is perhaps the most likely to be close to reality (DDM2 cross) the maximum likelihood value shifts to $r = 0.16_{-0.05}^{+0.06}$

Which value is proper to compare with Planck's $r<0.11$?

• As far as I know, Planck has not yet released any B-mode polarization data. Its value of r was calculated by trying to estimate the value of the amplitude of the tensor modes that is due to the interactions of the temperature-E modes and the temperature-temperature modes (E-E and T-B modes not producing any tensor amplitudes). But the strongest tensor mode amplitudes should come from the B-B mode interactions, which is what BICEP2 includes. So until Planck releases that data, I don't think we should be comparing the two r values – Jim Mar 20 '14 at 17:58
• thanks, I was seeing that South Pole Telescope reported r<0.13 and WMAP9 reported r<0.11 even prior to the Planck data arxiv.org/pdf/1305.3921.pdf. Would you say that the BICEP2 results completely supercede these results? – DavePhD Mar 20 '14 at 18:10
• I skimmed that paper and it seems they were doing predictions using best-fit parameters from WMAP9. That is not quite the same as results from experiment. As I said, Planck has not yet released all of its data on the B-mode polarization. So at the moment, it would seem that we should wait for the data before making many comparisons – Jim Mar 20 '14 at 18:27

The BICEP2 paper reports a tensor/scalar ratio r=0.20+0.07−0.05, but then says:

This is the value taken before corrections. There exist contributions to the B- mode due to changes in the photon polarization of the CMB while it is traveling before reaching the detector. The dust is the interstellar dust that has to be modeled.

Subtracting the various dust models and re-deriving the r constraint still results in high significance of detection. For the model which is perhaps the most likely to be close to reality (DDM2 cross) the maximum likelihood value shifts to r=0.16+0.06−0.05

Which value is proper to compare with Planck's r<0.11?

Assuming that Planck has corrected for the dust before giving its limit, ( a reasonable assumption since the existence of dust is known) it is the second value you have to compare with, which is different only by 1 sigma from the bound given by Planck, i.e. is consistent.

At these errors one does not call measurements definitive. Once many standard deviations separate old from new measurements, old ones can be ignored.

• ok, yes, I see now "Additional nuisance parameters are included to model ... the residual Galactic dust contribution" in the Planck paper. – DavePhD Mar 20 '14 at 18:39

Um, a snarky answer is that now neither is proper. As Anna notes, the $r=0.20$ value assumes no contribution from galactic dust polarized emissions ("foregrounds"), while $r=0.16$ results from BICEP2's indirect estimate of such foregrounds. However, now Planck has published a much more direct measurement of these dust emissions, and they're much higher than BICEP2 estimated. The residual significance may even be 0. See this question.

31 Jan 2015 update: And the residual significance is in fact 0. See update to my answer to the linked question.