12. CONCLUSIONS
We have described the observations, data reduction, simulation and power spectrum analysis of all three seasons of data taken by the BICEP2 experiment. The polarization maps presented here are the deepest ever made at degree angular scales having noise level of 87 nK-degrees in Q and U over an effective area of 380 square degrees.
To fully exploit this unprecedented sensitivity we have expanded our analysis pipeline in several ways. We have added an additional filtering of the timestream using a template temperature map (from Planck) to render the results insensitive to temperature to polarization leakage caused by leading order beam systematics. In addition we have implemented a map purification step that eliminates ambiguous modes prior to Bmode estimation. These deprojection and purification steps are both straightforward extensions of the kinds of linear filtering operations that are now common in CMB data analysis.
The power spectrum results are perfectly consistent with lensed-_CDM with one striking exception: the detection of a large excess in the BB spectrum in exactly the ` range where an inflationary gravitational wave signal is expected to peak. This excess represents a 5:2_ excursion from the base lensed- _CDM model. We have conducted a wide selection of jackknife tests which indicate that the B-mode signal is common on the sky in all data subsets. These tests offer very strong empirical evidence against a systematic origin for the signal.
In addition we have conducted extensive simulations using high fidelity per channel beam maps. These confirm our understanding of the beam effects, and that after deprojection of the two leading order modes, the residual is far below the level of the signal which we observe.
Having demonstrated that the signal is real and “on the sky” we proceeded to investigate if it may be due to foreground contamination. Polarized synchrotron emission from our galaxy is easily ruled out using low frequency polarized maps from WMAP. For polarized dust emission public maps are not yet available. We therefore investigate a range of models including new ones which use all of the information which is currently available from Planck. These models all predict auto spectrum power well below our observed level. In addition none of them show any significant cross correlation with our maps.
Taking cross spectra against 100 GHz maps from BICEP1 we find significant correlation and set a constraint on the spectral index of the signal consistent with CMB, and disfavoring synchrotron and dust by 2:3_ and 2:2_ respectively. The fact that the BICEP1 and Keck Array maps cross correlate is powerful further evidence against systematics.
The simplest and most economical remaining interpretation of the B-mode signal which we have detected is that it is due to tensor modes — the IGW template is an excellent fit to the observed excess. We therefore proceed to set a constraint on the tensor-to-scalar ratio and find r = 0:20+0:07 -0:05 with r = 0 ruled out at a significance of 7:0_. Multiple lines of evidence have been presented that foregrounds are a subdominant contribution: i) direct projection of the best available foreground models, ii) lack of strong cross correlation of those models against the observed sky pattern (Figure 6), iii) the frequency spectral index of the signal as constrained using BICEP1 data at 100 GHz (Figure 8 ), and iv) the spatial and power spectral form of the signal (Figures 3 and 10).
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 with r = 0 disfavored at 5:9_. These high values of r are in apparent tension with previous indirect limits based on temperature measurements and we have discussed some possible resolutions including modifications of the initial scalar perturbation spectrum such as running. However we emphasize that we do not claim to know what the resolution is.
Figure 14 shows the BICEP2 results compared to previous upper limits. The long search for tensor B-modes is apparently over, and a new era of B-mode cosmology has begun.
BICEP2 was supported by the US National Science Foundation under grants ANT-0742818 and ANT-1044978 (Caltech/Harvard) and ANT-0742592 and ANT-1110087 (Chicago/Minnesota). The development of antenna-coupled detector technology was supported by the JPL Research and Technology D evelopment Fund and grants 06-ARPA206- 0040 and 10-SAT10-0017 from the NASA APRA and SAT programs. The development and testing of focal planes were supported by the Gordon and Betty Moore Foundation at Caltech. Readout electronics were supported by a Canada Foundation for Innovation grant to UBC. The receiver development was supported in part by a grant from the W. M. Keck Foundation. The computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. Tireless administrative support was provided by Irene Coyle and KathyDeniston.
We thank the staff of the US Antarctic Program and in particular the South Pole Station without whose help this research would not have been possible. We thank all those who have contributed past efforts to the BICEP/Keck Array series of experiments, including the BICEP1 and Keck Arrayn teams. We dedicate this paper to the memory of Andrew Lange, whom we sorely miss.
FIG. 13.— Indirect constraints on r from CMB temperature spectrum measurements relax in the context of various model extensions. Shown here is one example, following Planck Collaboration XVI (2013) Figure 23, where tensors and running of the scalar spectral index are added to the base _CDM model. The contours show the resulting 68% and 95% confidence regions for r and the scalar spectral index ns when also allowing running. The red contours are for the “Planck+WP+highL” data combination, which for this model extension gives a 95% bound r < 0:26 (Planck Collaboration XVI 2013). The blue contours add the BICEP2 constraint on r shown in the center panel of Figure 10. See the text for further details.
FIG. 14.— BICEP2 BB auto spectra and 95% upper limits from several previous experiments (Leitch et al. 2005; Montroy et al. 2006; Sievers et al. 2007; Bischoff et al. 2008; Brown et al. 2009; QUIET Collaboration et al. 2011, 2012; Bennett et al. 2013; Barkats et al. 2014). The curves show the theory expectations for r = 0:2 and lensed-_CDM.
