Constraints on Primordial Gravitational Waves Using $Planck$, WMAP, and New BICEP2/$Keck$ Observations through the 2015 Season

We present results from an analysis of all data taken by the bicep2/Keck CMB polarization experiments up to and including the 2015 observing season. This includes the first Keck Array observations at 220 GHz and additional observations at 95 and 150 GHz. The Q and U maps reach depths of 5.2, 2.9, and $26\mu {\mathrm{K}}_{\mathrm{CMB}}\mathrm{arcmin}$ at 95, 150, and 220 GHz, respectively, over an effective area of $\approx 400$ square degrees. The 220 GHz maps achieve a signal to noise on polarized dust emission approximately equal to that of Planck at 353 GHz. We take auto and cross spectra between these maps and publicly available WMAP and Planck maps at frequencies from 23 to 353 GHz. We evaluate the joint likelihood of the spectra versus a multicomponent model of lensed-$\mathrm{\Lambda }\mathrm{CDM}+r+\text{dust}+\text{synchrotron}+\text{noise}$. The foreground model has seven parameters, and we impose priors on some of these using external information from Planck and WMAP derived from larger regions of sky. The model is shown to be an adequate description of the data at the current noise levels. The likelihood analysis yields the constraint $r_{0.05}<0.07$ at 95% confidence, which tightens to $r_{0.05}<0.06$ in conjunction with Planck temperature measurements and other data. The lensing signal is detected at $8.8\sigma$ significance. Running a maximum likelihood search on simulations we obtain unbiased results and find that $\sigma (r)=0.020$. These are the strongest constraints to date on primordial gravitational waves.

Figure 1

Maps of degree angular scale $E$ modes ($50<\ell <120$) at three frequencies made using Keck Array data from the 2015 season only. The similarity of the pattern indicates that $\mathrm{\Lambda }\mathrm{CDM}$ $E$ modes dominate at all three frequencies (and that the signal to noise is high). The color scale is in $\mu \mathrm{K}$, and the range is allowed to vary slightly to (partially) compensate for the decrease in beam size with increasing frequency.

Figure 2

$EE$ and $BB$ auto and cross spectra calculated using bicep2/Keck 95, 150, and 220 GHz maps and the Planck 353 GHz map. The bicep2/Keck maps use all data taken up to and including the 2015 observing season—we refer to these as BK15. The black lines show the model expectation values for lensed $\mathrm{\Lambda }\mathrm{CDM}$, while the red lines show the expectation values of the baseline lensed-$\mathrm{\Lambda }\mathrm{CDM}+\text{dust}$ model from our previous BK14 analysis ($r=0$, $A_{d,353}=4.3\mu {\mathrm{K}}^2$, ${\beta }_d=1.6$, ${\alpha }_d=-0.4$), and the error bars are scaled to that model. Note that the model shown was fit to $BB$ only and did not use the 220 GHz points (which are entirely new). The agreement with the spectra involving 220 GHz and all the $EE$ spectra (under the assumption that $EE/BB=2$ for dust) is therefore a validation of the model. (The dashed red lines show the expectation values of the lensed-$\mathrm{\Lambda }\mathrm{CDM}+\text{dust}$ model when adding strong spectral decorrelation of the dust pattern—see Appendix F in the Supplemental Material [20] for further information.)

Figure 3

Upper panel: The noise spectra of the BK15 maps for 95 (red), 150 (green), and 220 GHz (blue) after correction for the filtering of signal, which occurs due to the beam roll-off and time stream filtering. (Note that no ${\ell }^2$ scaling is applied.) Lower panel: The effective sky fraction as calculated from the ratio of the mean noise realization band powers to their fluctuation $f_{\text{sky}}(\ell )=(1/2\ell \mathrm{\Delta }\ell ){[\sqrt{2}\overline{N_b}/\sigma (N_b)]}^2$, i.e., the observed number of $B$ mode degrees of freedom divided by the nominal full-sky number. The turn down at low $\ell$ is due to mode loss to the time stream filtering and matrix purification.

Figure 4

Results of a multicomponent multispectral likelihood analysis of bicep2/$Keck+\mathrm{WMAP}\text{/}Planck$ data. The red faint curves are the baseline result from the previous BK14 paper (the black curves from Fig. 4 of that paper). The bold black curves are the new baseline BK15 results. Differences between these analyses include adding Keck Array data taken during the 2015 observing season, in particular doubling the 95 GHz sensitivity and adding, for the first time, a 220 GHz channel. (In addition the $\epsilon$ prior is modified.) The upper limit on the tensor-to-scalar ratio tightens to $r_{0.05}<0.072$ at 95% confidence. The parameters $A_d$ and $A_{\text{sync}}$ are the amplitudes of the dust and synchrotron $B$-mode power spectra, where $\beta$ and $\alpha$ are the respective frequency and spatial spectral indices. The correlation coefficient between the dust and synchrotron patterns is $\epsilon$. In the $\beta$, $\alpha$, and $\epsilon$ panels the dashed lines show the priors placed on these parameters (either Gaussian or uniform). Broadening or tightening the uniform prior range on ${\alpha }_s$ and ${\alpha }_d$ results in very small changes, and negligible changes to the $r$ constraint.

Figure 5

Constraints in the $r$ vs $n_s$ plane when using Planck 2015 plus additional data, and when also adding bicep2/Keck data through the end of the 2015 season—the constraint on $r$ tightens from $r_{0.05}<0.12$ to $r_{0.05}<0.06$. This figure is adapted from Fig. 21 of Ref. [3], with two notable differences: switching lowP to lowT plus a $\tau$ prior of $0.055\pm 0.009$ Ref. [50], and the exclusion of JLA data and the $H_0$ prior.

Figure 6

Expectation values and noise uncertainties for the $\ell \sim 80$ $BB$ band power in the bicep2/Keck field. The solid and dashed black lines show the expected signal power of lensed-$\mathrm{\Lambda }\mathrm{CDM}$ and $r_{0.05}=0.05$ and 0.01. Since CMB units are used, the levels corresponding to these are flat with frequency. The blue and red bands show the 1 and $2\sigma$ ranges of dust and synchrotron in the baseline analysis including the uncertainties in the amplitude and frequency spectral index parameters ($A_{\text{sync},23}$, ${\beta }_s$, and $A_{d,353}$, ${\beta }_d$). The bicep2/Keck auto-spectrum noise uncertainties are shown as large blue circles, and the noise uncertainties of the WMAP/Planck single-frequency spectra evaluated in the bicep2/Keck field are shown in black. The blue crosses show the noise uncertainty of selected cross spectra, and are plotted at horizontal positions such that they can be compared vertically with the dust and sync curves.