Reanalysis of the BICEP2, Keck and Planck Data: No Evidence for Gravitational Radiation

A joint analysis of data collected by the Planck and BICEP2+Keck teams has previously given $r = 0.09^{+0.06}_{-0.04}$ for BICEP2 and $r = 0.02^{+0.04}_{-0.02}$ for Keck. Analyzing BICEP2 using its published noise estimate, we had earlier (Colley & Gott 2015) found $r = 0.09 \pm 0.04$, agreeing with the final joint results for BICEP2. With the Keck data now available, we have done something the joint analysis did not: a correlation study of the BICEP2 vs. Keck B-mode maps. Knowing the correlation coefficient between the two and their amplitudes allows us to determine the noise in each map (which we check using the E-modes). We find the noise power in the BICEP2 map to be twice the original BICEP2 published estimate, explaining the anomalously high $r$ value obtained by BICEP2. We now find $r = 0.004 \pm 0.04$ for BICEP2 and $r = -0.01 \pm 0.04$ for Keck. Since $r \ge 0$ by definition, this implies a maximum likelihood value of $r = 0$, or no evidence for gravitational waves. Starobinsky Inflation ($r = 0.0036$) is not ruled out, however. Krauss & Wilzcek (2014) have already argued that "measurement of polarization of the CMB due to a long-wavelength stochastic background of gravitational waves from Inflation in the early Universe would firmly establish the quantization of gravity," and, therefore, the existence of gravitons. We argue it would also constitute a detection of gravitational Hawking radiation (explicitly from the causal horizons due to Inflation).