The recent indications for a tensor-to-scalar ratio r \simeq 0.2 from BICEP2 measurements of the cosmic microwave background ( CMB ) B-mode polarization present some tension with upper limits r \lesssim 0.1 from measurements of CMB temperature fluctuations .
Here we point out that tensor perturbations can induce B modes in the CMB polarization without inducing any temperature fluctuations nor E-mode polarization whatsoever , but only , at the expense of violating the Copernican principle .
We present this mathematical possibility as a new ingredient for the model-builder ’ s toolkit in case the tension between B modes and temperature fluctuations can not be resolved with more conventional ideas .