Measurement of the Cosmic Microwave Background Polarization Lensing Power Spectrum with the POLARBEAR Experiment

Gravitational lensing due to the large-scale distribution of matter in the cosmos distorts the primordial cosmic microwave background (CMB) and thereby induces new, small-scale $B$-mode polarization. This signal carries detailed information about the distribution of all the gravitating matter between the observer and CMB last scattering surface. We report the first direct evidence for polarization lensing based on purely CMB information, from using the four-point correlations of even- and odd-parity $E$- and $B$-mode polarization mapped over $\sim 30$ square degrees of the sky measured by the POLARBEAR experiment. These data were analyzed using a blind analysis framework and checked for spurious systematic contamination using null tests and simulations. Evidence for the signal of polarization lensing and lensing $B$ modes is found at $4.2\sigma$ ($\mathrm{stat}+\text{sys}$) significance. The amplitude of matter fluctuations is measured with a precision of 27%, and is found to be consistent with the Lambda cold dark matter cosmological model. This measurement demonstrates a new technique, capable of mapping all gravitating matter in the Universe, sensitive to the sum of neutrino masses, and essential for cleaning the lensing $B$-mode signal in searches for primordial gravitational waves.

Figure 1

Curl null power spectra for each of the three patches for the $⟨EEEB⟩$ and $⟨EBEB⟩$ estimators. The patch-combined curl null power spectra are shown in red for the two lensing estimators. All the curl null power spectra are consistent with zero.

Figure 2

Measured polarization lensing power spectra for each of POLARBEAR’s three patches, for both lensing estimators $⟨EEEB⟩$ (left) and $⟨EBEB⟩$ (right). The lensing signal predicted by the $\mathrm{\Lambda }\text{CDM}$ model is shown as the solid black curve. The measured lensing power spectra are shown for each patch in dark green (RA23), blue (RA12), and magenta (RA4.5), respectively, and are offset in $L$ slightly for clarity. The patch-combined lensing power spectrum is shown in red.

Figure 3

Polarization lensing power spectra co-added from the three patches and two estimators are shown in red. The lensing signal predicted by the $\mathrm{\Lambda }\text{CDM}$ model is shown as the dashed black curve in the left panel and the solid black curve in the right panel, respectively. The polarization lensing power spectrum $⟨EEEB⟩$ is in blue and $⟨EBEB⟩$ dark green. Left: A $4.2\sigma$ rejection of the null hypothesis of no lensing. These data indicate a lensing amplitude $\mathcal{A}=1.37\pm 0.30\pm 0.13$ normalized to the fiducial $\mathrm{\Lambda }\text{CDM}$ value. Right: The same data, assuming the existence of gravitational lensing to calculate error bars, including sample variance and including the covariance between $⟨EEEB⟩$ and $⟨EBEB⟩$. In this case, the lensing amplitude is measured as $\mathcal{A}=1.06\pm {0.47}_{-0.31}^{+0.35}$, corresponding to 54% uncertainty on the $C_L^{dd}$ power spectrum (27% uncertainty on the amplitude of matter fluctuations). The histograms of the amplitudes $\mathcal{A}$ from 500 unlensed and lensed simulations are shown in the inset boxes.